■ >''.. 






imi 



'.> >: 






i»V) 



fin. 















X }'^ 






>.* L ^ 1 t ^ 



'\ 




A^' 



'b^ 



■^^^ v^' 









^0 o 11 tj/-?^^; 



^m-^-" 

\>-:..,, ,^^ 



%:M'-'- 



■ o 



' 3 \ ^' 






c^-" 



.0 Ni (' 



'-"■/ /it 



,^\ 



O^ 






..V^'\^^ 



^^ 









<f. 






^^y- 





' , . - VN 



^./V"'-"^.'^^ ,>'».<'..'•' 







t%., V'^f'W. 









* 0-, 













UNIVERSITY MANUALS 
EDITED BY PROFESSOR KNIGHT 



LOGIC 

INDUCTIVE AND DEDUCTIVE 



Published May, 1893 

Reprinted December, 1893 
November^ 1894 
January, 1899 
August, 1904 
June, 1909 
September 19 12 
July, 1913 
January 191 5 



LOGIC 

INDUCTIVE AND DEDUCTIVE 



BY WILLIAM MINTO, M.A. 

I! 
HON. LL.D., ST. ANDREWS 

Late Professor op Logic in the University of Aberdiem 



NEW YORK 

CHARLES SCRIBNER'S SONS 

1915 









PRINTED IN GREAT BRITAIN BY 
THE EDINBURGH PRESS, Q AND LI YOUNG STREET, EDINBURGH 



PREFACE. 

In this little treatise two things are attempted 
that at first might appear incompatible. One 
of them is to put the study of logical formulae 
on a historical basis. Strangely enough, the 
scientific evolution of logical forms, is a bit of 
history that still awaits the zeal and genius of 
some great scholar. I have neither ambition 
nor qualification for such a magnum opus, and 
my life is already more than half spent; but the 
gap in evolutionary research is so obvious that 
doubtless some younger man is now at work in 
the field unknown to me. All that I can hope to 
do is to act as a humble pioneer according to 
my imperfect lights. Even the little I have done 
represents work begun more than twenty years 
ago, and continuously pursued for the last twelve 
years during a considerable portion of my time. 

The other aim, which might at first appear 
inconsistent with this, is to increase the power 
of Logic as a practical discipline. The main 
purpose of this practical science, or scientific 
art, is conceived to be the organisation of reason 
against error, and error in its various kinds is 
made the basis of the division of the subject. To 
carry out this practical aim along with the histori- 
cal one is not hopeless, because throughout its 

(▼) 



?i Preface, 

long history Logic has been a practical science; 
and, as I have tried to show at some length in 
introductory chapters, has concerned itself at 
different periods with the risks of error peculiar 
to each. 

To enumerate the various books, ancient and 
modern, to which I have been indebted, would be 
a vain parade. Where I have consciously adopted 
any distinctive recent contribution to the long line 
of tradition, I have made particular acknowledg- 
ment. My greatest obligation is to my old pro- 
fessor, Alexander Bain, to whom I owe my first 
interest in the subject, and more details than I 
can possibly separate from the general body of my 
knowledge. 

W. M. 

Aberdeen, January, iSgj* 



Since these sentences were written, the author of 
this book has died ; and Professor Minto's Logic 
is his last contribution to the literature of his 
country. It embodies a large part of his teaching 
in the philosophical class-room of his University, 
and doubtless reflects the spirit of the whole of it. 

Scottish Philosophy has lost in him one of its 
typical representatives, and the University of the 
North one of its most stimulating teachers. There 
have been few more distinguished men than 
William Minto in the professoriate ol Aberdeen ; 
and the memory of what he was, of his wide and 
varied learning, ms brilliant conversation, his 
urbanity, and his rare power of sympathy with 
men with whose opinions he did not agree, will 
remain a possession to many who mourn his loss. 

It will be something if this little book keeps his 
memory alive, both amongst the students who 
owed so much to him, and in the large circle of 
friends who used to feel the charm of his 
personality. 

WILLIAM KNIGHT. 



GENERAL PLAN OF THE SERIES. 



This Series is primarily designed to aid the University Extension 
Movement throughout Great Britain and America^ and to supply 
the need so widely felt by students^ of Text-books for study and 
reference f in connexion with the authorised Courses of Lectures, 

The Manuals differ from those already in existence in that they 
are not intended for School use, or for Examination purposes ; and 
that their aim is to educate, rather than to inform. The statement 
of details is meant to illustrate the working of general laws, and the 
development of principles ; while the historical evolution of the 
subject dealt with is kept in view, along with its philosophical 
significance. 

The remarkable success which has attended University Extension 
in Britain has been partly due to the combination of scientific treat' 
ment with popularity, and to the union of simplicity with thorough' 
ness. This movement, however, can only reach those resident in the 
larger centres of population, while all over the country there are 
thoughtful persons who desire the same kind of teaching. It is for 
them also that this Series is designed. Its aim is to supply thi 
general reader with the same kind of teaching as is given in the 
Lectures, and to reflect the spirit which has characterised the movC' 
ment, via,, the combination of principles with facts, and of methods 
with results. 

The Manuals are also intended to be contributions to the Literature 
of the Subjects with which they respectively deal, quite apart from 
University Extension ; and some of them will he found to meet a 
general rather than a special want. 

They will be issued simultaneously in England and America. 
Volumes dealing with separate sections of Literature, Science^ 
Philosophy, History, and Art have been assigned to representative 
literary men, to University Professors, or to Extension Lecturers 
connected with Oxford, Cambridge, London, and the Universities of 
Scotland and Ireland. 

A list of the works in this Series will be found at the end ofth^ 
volume. 



CONTENTS, 

INTRODUCTION. 



The Origin and Scope of Logic, ---••- i 

11. 

Logic as a Preventive of Error or Fallacy — The Inner 

Sophist, 17 

IIL 

The Axioms of Dialectic and of Syllogism, - « - - 2g 

BOOK I. 

THE LOGIC OF CONSISTENCY— SYLLOGISM AND 
DEFINITION. 

PART L 
THE ELEMENTS OF PROPOSITIONS. 

Chapter L 

General Names and Allied Distinctions, - - - - 43 

Chapter IL 

The Syllogistic Analysis of Propositions into Terms, (i) 
The Bare Analytic Forms. (2) The Practice of Syllo- 
gistic Analysis. (3) Some Technical Difficulties, - - 62 
(ix) 



PART IL 

DIFINITION, 
Ckaptbr I. 

fAGB 

(i) Imperfect Understanding of Words. (2) Verification of 
the Meaning— Dialectic. (3) Fixation of the Meaning 
—Division or Classiftcation, Definition, Naming, - . 8a 

Chapter II. 
The Five Prcdicables— Verbal and Real Predication, - • 105 

Chapter III. 
Aristotle's Categories, - - . - - . •112 

Chapter IV. 
The Controversy about Universals— Difficulties concerning 

the Relation of General Names to Thought and to Reality, 120 

PART III, 

THE INTERPRETATION OF PROPOSITIONS. 

Chapter I. 

Theories of Predication — ^Theories of Judgment, - . - 131 

Chapter II. 

The " Opposition " of Propositions—The Interpretation of 
" No " - - - 

Chapter III. 
The Implication of Propositions — Immediate Formal Infe- 

rence — Eduction, .146 

Chapter IV, 
The Counter-Implication of Propositions, - • » • Xr6 

PART IV. 

THE INTERDEPENDENCE OF PROPOSITION& 

Chaptsr !• 

The Syllogiim, g^^ 



Contents. ■ xi 

Chapt£r II. 

PAGB 

The Figures and Moods of the Syllogism, (i) The First 
Figure. (2) The Minor Figures and their Reduction to 
the First. (3) Sorites, ^73 

Chapter III. 
The Demonstration of the Syllogistic Moods — The Canons 

of the Syllogism, - - - 185 

Chapter IV. -, 

The Analysis of Arguments into Syllogistic Forms, - * 196 

Chapter V. 
Enth3rmeme8, .---••«.• 205 

Chapter VI. 
The Utility of the Syllogism, -.---„- 2og 

Chapter VII. 

Conditional Arguments — Hypothetical Syllogism, Disjunctive 

Syllogism and Dilemma, - 215 

Chapter VIII. 
Fallacies in Deductive Argument — Petitio Principii and 

Ignoratio Elenchi^ 226 

Chapter IX. 
Formal or Aristotelian Induction — Inductive Argument — 

The Inductive Syllogism, 235 

BOOK II. 

INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE. 

Introduction, 243 

Chapter I. 
The Data of Experience as Grounds of Inference or Rational 

Belief, 273 

Chapter II. 
Ascertainment of Simple Facts in their Order — Personal 
Observation — Hearsay Evidence — Method of Testing 
Traditional Evidence, - - ^^ . ., . . 385 



3cii Contenh. 

Chapter III, 

PAGS 

Ascertainment of Facts of Causation, (i) Po^i Hoc Ergo 
Propter Hoc, (2) Meaning of Cause — Methods of Ob- 
servation — Miirs Experimental Methods, - - - 295 

Chapter IV. 
Methods of Observation — Single Difference, (i) The Prin- 
ciple of Single Difference. (2) Application of the 
Principle, .--- 308 

Chapter V. 

Methods of Observation — Elimination — Single Agreement, 
(i) The Principle of Elimination. (2) The Principle of 
Single Agreement. (3) Mill's " Joint Method of Agree- 
ment and Difference," ---«.-- 318 

Chapter VL 
Methods of Observation — Minor Methods, (x) Concomitant 

Variations. (2) Single Residue, - - - - - 329 

Chapter VII. 

The Method of Explanation, (i) The Four Stages of Orderly 
Procedure. (2) Obstacles to Explanation — Plurality of 
Causes and Intermixture of Effects. (3) The Proof of a 
Hypothesis, 334 

Chapter VIII. 

Supplementary Methods of Investigation, (i) The Main- 
tenance of Averages — Supplement to the Method of 
Difference. (2) The Presumption from Extra-Casual 
Coincidence, - 35^ 

Chapter IX. 

Probable Inference to Particulars — The Measurement of 

Probability, - ■ 362 

Chapter X. 

Inference from Analogy, .----.. 367 



introduction; 



L— THE ORIGIN AND SCOPE OF LOGIC. 

The question has sometimes been asked, Where should 
we begin in Logic ? Particularly within the present 
century has this difficulty been felt, when the study 
of Logic has been revived and made intricate by the 
different purposes of its cultivators. 

Where did the founder of Logic begin ? Where did 
Aristotle begin ? This seems to be the simplest way 
of settling where we should begin, for the system 
shaped by Aristotle is still the trunk of the tree, 
though there have been so many offshoots from the 
old stump and so many parasitic plants have wound 
themselves round it that Logic is now almost as 
tangled a growth as the Yews of Borrowdale — 

An intertwisted mass of fibres serpentine 
Upcoiling and inveterately convolved. 

It used to be said that Logic had remained for two 
thousand years precisely as Aristotle left it. It was 
an example of a science or art perfected at one stroke 
by the genius of its first inventor. The bewildered 
student must often wish that this were so : it is only 
superficially true. Much of Aristotle's nomenclature 
and his central formulae have been retained, but they 

X 



2 Introduction. 

have been very variously supplemented and interpreted 
to very different purposes — often to no purpose at all. 

The Cambridge mathematician's boast about his 
new theorem — "The best of it all is that it can 
never by any possibility be made of the slightest use 
to anybody for anything " — might be made with truth 
about many of the later developments of Logic. We 
may say the same, indeed, about the later develop- 
ments of any subject that has been a playground for 
generation after generation of acute intellects, happy in 
their own disinterested exercise. Educational subjects 
— subjects appropriated for the general schooling of 
young minds — are particularly apt to be developed 
out of the lines of their original intention. So many 
influences conspire to pervert the original aim. The 
convenience of the teacher, the convenience of the 
learner, the love of novelty, the love of symmetry, 
the love of subtlety ; easy-going indolence on the one 
hand and intellectual restlessness on the other — all 
these motives act from within on traditional matter 
without regard to any external purpose whatever. 
Thus in Logic difficulties have been glossed over and 
simplified for the dull understanding, while acute minds 
have revelled in variations and new and ingenious 
manipulations af the old formulae, and in multiplication 
and more exact and symmetrical definition of the old 
distinctions. 

To trace the evolution of the forms and theories of 
Logic under these various influences during its periods 
of active development is a task more easily conceived 
than executed, and one far above the ambition of an 
introductory treatise. But it is well that even he who 
writes for beginners should recognise that the forms 
now commonly used have been evolved out of a 



The Origin and Scope of Logic. 3 

simpler tradition. Without entering into the details 
of the process, it is possible to indicate its main stages, 
and thus furnish a clue out of the modern labyrinthine 
confusion of purposes. 

How did the Aristotelian Logic originate ? Its 
central feature is the syllogistic forms. In what 
circumstances did Aristotle invent these ? For what 
purpose ? What use did he contemplate for them ? 
In rightly understanding this, we shall understand 
the original scope or province of Logic, and thus be 
in a position to understand more clearly how it has 
been modified, contracted, expanded, and supple- 
mented. 

Logic has always made high claims as the sdentia 
scientiarum^ the science of sciences. The builders of 
this Tower of Babel are threatened in these latter days 
with confusion of tongues. We may escape this 
danger if we can recover the designs of the founder, 
and of the master-builders who succeeded him. 

Aristotle's Logic has been so long before the world 
in abstract isolation that we can hardly believe that its 
form was in any way determined by local accident. A 
horror as of sacrilege is excited by the bare suggestion 
that the author of this grand and venerable work, 
one of the most august monuments of transcendent 
intellect, was in his day and generation only a pre- 
eminent tutor or schoolmaster, and that his logical 
writings were designed for the accomplishment of his 
pupils in a special art in which every intellectually 
ambitious young Athenian of the period aspired to 
excel. Yet such is the plain fact, baldly stated. 
Aristotle's Logic in its primary aim was as practical 
as a treatise on Navigation, or ** Caven'disfr"~Dn 
Whist", The latter is the more exact of the two 



4 Introduction, 

comparisona It was in effect in its various parts a 
series of handbooks for a temporarily fashionable intel- 
lectual game, a peculiar mode of disputation or dialectic,* 
the game of Question and Answer, the game so fully 
illustrated in the Dialogues of Plato, the game identi- 
fied with the name of Socrates. 

We may lay stress, if we like, on the intellectuality 
of the game, and the high topics on which it was 
exercised. It was a game that could flourish only 
among a peculiarly intellectual people ; a people less 
acute would find little sport in it. The Athenians 
still take a singular delight in disputation. You 

1 We know for certain — and it is one of the evidences of the 
importance attached to this trivial-looking pastime — that two ol 
the great teacher's logical treatises, the Topics and the Sophistical 
Refutations, were written especially for the guidance of Ques* 
tioners and Respondents. The one instructs the disputant how ta 
qualify himself methodically for discussion before an ordinarj^ 
audience, when the admissions extracted from the respondent are 
matters of common belief, the questioner's skill being directed to 
make it appear that the respondent's position is inconsistent with 
these. The other is a systematic exposure of sophistical tricks, 
mostly verbal quibbles, whereby a delusive appearance of victory 
in debate may be obtained. But in the concluding chapter of the 
Elenchi, where Aristotle claims not only that his method is 
superior to the empirical methods of rival teachers, but that 
it is entirely original, it is the Syllogism upon which he lays 
stress as his peculiar and chief invention. The Syllogism, the 
pure forms of which are expounded in his Prior Analytics, is really 
the centre of Aristotle's logical system, whether the propositions 
to which it is applied are matters of scientific truth as in the Pos- 
terior Analytics, or matters of common opinion as in the Topics. 
The treatise on Interpretation, i,e,t the interpretation of the 
Respondent's *' Yes " and " No," is preliminary to the Syllogism, 
the reasoning of the admissions together. Even in the half- 
grammatical half-logical treatise on the Categories, the author 
always keeps an eye on the Syllogistic analysis. 



The Origin and Scope of Legit. 5 

cannot visit Athens without being struck by it. You 
may still see groups formed round two protagonists 
in the caf^s or the squares, or among the ruins of 
the Acropolis, in a way to remind you of Socrates 
and his friends. They do not argue as Gil Bias and 
his Hibernians did with heat and temper, ending 
in blows. They argue for the pure love of arguing, 
the audience sitting or standing by to see fair play 
with the keenest enjoyment of intellectual thrust 
and parry. No other people could argue like the 
Greeks without coming to blows. It is one of theii 
characteristics now, and so it was in old times two 
thousand years ago. And about a century before 
Aristotle reached manhood, they had invented this 
peculiarly difficult and trying species of disputative 
pastime, in which we find the genesis of Aristotle's 
togical treatises. 

To get a proper idea of this debate by Question and 
Answer, which we may call Socratic disputation after 
its most renowned master, one must read some of the 
dialogues of Plato. I will indicate merely the skeleton 
of the game, to show how happily it lent itself to 
Aristotle's analysis of arguments and propositions. 

A thesis or proposition is put up for debate, e,g.^ that 
knowledge is nothing else than sensible perception,* that 
it is a greater evil to do wrong than to suffer wrong,' 
that the love of gain is not reprehensible.^ There are 
two disputants, but they do not speak on the question 
by turns, so many minutes being allowed to each as 
in a modern encounter of wits. One of the two, who 
may be called the Questioner, is limited to asking 

^ Thesetetus, 151 E. * Gorgias, 473 D. 

• Hipparcbusij 225 A. 



6 Introduction. 

questions, the other, the Respondent, is limited to 
answering. Further, the Respondent can answer only 
** Yes " or " No," with perhaps a little explanation : 
on his side the Questioner must ask only questions 
that admit of the simple answer "Yes" or "No". 
The Questioner's business is to extract from the 
Respondent admissions involving the opposite of what 
he has undertaken to maintain. The Questioner tries 
in short to make him contradict himself. Only a 
very stupid Respondent would do this at once : the 
Questioner plies him with general principles, analogies, 
plain cases ; leads him on from admission to admission, 
and then putting the admissions together convicts him 
iout of his own mouth of inconsistency.* 

Now mark precisely where Aristotle struck in with 
his invention of the Syllogism, the invention on which 
he prided himself as specially his own, and the forms 
of which have clung to Logic ever since, even in the 
usage of those who deride Aristotle's Moods and Figures 
as antiquated superstitions. Suppose yourself the 
Questioner, where did he profess to help you with his 
mechanism? In effect, as the word Syllogism indicates, 
it was when you had obtained a number of admissions, 

^ In its leading and primary use, this was a mode of debate, a 
duel of wits, in which two men engaged before an audience. But 
the same form could be used, and was used, notably by Socrates, 
not in an eristic spirit but as a means of awakening people to the 
consequences of certain admissions or first principles, and thus 
making vague knowledge explicit and clear. The mind being 
detained on proposition after proposition as assent was given to 
it, dialectic was a valuable instrument of instruction and exposition. 
But whatever the purpose of the exercise, controversial triumph, 
or solid grounding in first principles — "the evolution of in-dwelling 
conceptions" — the central interest lay in the syllogising or reasoning 
together of the separately assumed or admitted propositions* 



The Origin and Scope of Logic. 7 

and wished to reason them together, to demonstrate 
how they bore upon the thesis in dispute, how they 
hung together, how they necessarily involved what 
you were contending for. And the essence of his 
mechanism was the reduction of the admitted proposi- 
tions to common terms, and to certain types or forms 
which are manifestly equivalent or inter-dependent. 
Aristotle advised his pupils also in the tactics of the 
game, but his grand invention was the form or type oi 
admissions that you should strive to obtain, and the 
effective manipulation of them when you had got 
them. 

An example will show the nature of this help, and 
what it was worth. To bring the thing nearer home, 
let us, instead of an example from Plato, whose topics 
often seem artificial to us now, take a thesis from last 
century, a paradox still arguable, Mandeville's famous 
— some would say infamous — paradox that Private 
Vices are Public Benefits. Undertake to maintain this, 
and you will have no difficulty in getting a respondent 
prepared to maintain the negative. The plain men, 
such as Socrates cross-questioned, would have declared 
at once that a vice is a vice, and can never do any good 
to anybody. Your Respondent denies your proposi- 
tion simply : he upholds that private vices never are 
public benefits, and defies you to extract from him any 
admission inconsistent with this. Your task then is to 
lure him somehow into admitting that in some cases 
what is vicious in the individual may be of service to 
the State. This is enough : you are not concerned to 
establish that this holds of all private vices. A single 
instance to the contrary is enough to break down his 
universal negative. You cannot, of course, expect 
him to make the necessary admission in direct terms : 



8 iniroductiofu 

you must go round about. You know, perhaps, that 
he has confidence in Bishop Butler as a moralist. You 
try him with the saying : " To aim at public and 
private good are so far from being inconsistent that 
they mutually promote each other''. Does he admit 
this? 

Perhaps he wants some little explanation or exempli- 
fication to enable him to grasp your meaning. This 
was within the rules of the game. You put cases to 
him, asking for his ** Yes '' or " No " to each. Suppose 
a man goes into Parliament, not out of any zeal for 
the public good, but in pure vainglory, or to serve his 
private ends, is it possible for him to render the State 
good service ? Or suppose a milk- seller takes great 
pains to keep his milk pure, not because he cares for 
the public health, but because it pays, is this a benefit 
to the public ? 

Let these questions be answered in the affirmative, 
putting you in possession of the admission that some 
actions undertaken for private ends are of public 
advantage, what must you extract besides to make good 
your position as against the Respondent ? To see 
clearly at this stage what now is required, though you 
have to reach it circuitously, masking your approach 
under difference of language, would clearly be an 
advantage. This was the advantage that Aristotle's 
method offered to supply. A disputant familiar with 
his analysis would foresee at once that if he could get 
the Respondent to admit that all actions undertaken 
for private ends are vicious, the victory was his, while 
nothing short of this would serve. 

Here my reader may interject that he could have 
seen this without any help from Aristotle, and that 
anybody may see it without knowing that what he has 



77u Origin and Scope of Logic. 9 

to do is, in Aristotelian language, to construct a syllo- 
gism in Bokardo. I pass this over. I am not con- 
cerned at this point to defend the utility of Aristotle*s 
method. All that I want is to illustrate the kind of 
use that it was intended for. Perhaps if Aristotle had 
not habituated men's minds to his analysis, we should 
none of us have been able to discern coherence and 
detect incoherence as quickly and clearly as we do now. 
But to return to our example. As Aristotle's pupil, 
^^ou would have seen at the stage we are speaking of 
Ihat the establishment of your thesis must turn upon 
the definition of virtue and vice. You must proceed, 
therefore, to cross-examine your Respondent about 
this. You are not allowed to ask him what he means 
by virtue, or what he means by vice. In accordance 
with the rules of the dialectic, it is your business to 
propound definitions, and demand his Yes or No to 
them. You ask him, say, whether he agrees with 
Shaftesbury's definition of a virtuous action as an 
action undertaken purely for the good of others. If 
he assents, it follows that an action undertaken with 
any suspicion of a self-interested motive cannot be 
numbered among the virtues. If he agrees, further, 
that every action must be either vicious or virtuous, 
you have admissions sufficient to prove your original 
thesis. All that you have now to do to make your 
triumph manifest, is to display the admissions you 
have obtained in common terms. 

Some actions done with a self-interested motive are public 

benefits. 
All actions done with a self-interested motive are private 

vices. 

From these premisses it follows irresistibly that 
Some private vices ace public benefits. 



lo Introduction, 

This illustration may serve to show the kind of 
disputation for which Aristotle's logic was designed, 
and thus to make clear its primary uses and its 
limitations. 

To realise its uses, and judge whether there is 
anything analogous to them in modern needs, con- 
ceive the chief things that it behoved Questioner 
and Respondent in this game to know. All that a 
proposition necessarily implies ; all that two proposi- 
tions put together imply; on what conditions and 
to what extent one admission is inconsistent with 
another ; when one admission necessarily involves 
another ; when two necessarily involve a third. And 
to these ends it was obviously necessary to have an 
exact understanding of the terms used, so as to avoid 
the snares of ambiguous language. 
\ That a Syllogistic or Logic of Consistency should 
emerge out of Yes -and -No Dialectic was natural. 
Things in this world come when they are wanted : 
inventions are made on the spur of necessity. It was 
above all necessary in this kind of debate to avoid 
contradicting yourself : to maintain your consistency. 
A clever interrogator spread out proposition after pro- 
position before you and invited your assent, choosing 
forms of words likely to catch your prejudices and lure 
you into self-contradiction. An organon, instrument, 
or discipline calculated to protect you as Respondent 
and guide you as Questioner by making clear what an 
admission led to, was urgently called for, and when 
the game had been in high fashion for more than a 
century Aristotle's genius devised what was wanted, 
^ meeting at the same time, no doubt, collateral needs 
that had arisen from the application of Dialectic to 
various kinds of subject-matter. 



The Origin and Scope of Logic, ii 

The thoroughness of Aristotle's system was doubt- 
less due partly to the searching character of the 
dialectic in which it had its birth. No other mode of 
disputation makes such demands upon the disputant's 
intellectual agility and precision, or is so well adapted 
to lay bare the skeleton of an argument. 

The uses of Aristotle's logical treatises remained 
when the fashion that had called them forth had 
passed.^ Clear and consistent thinking, a mastery of 
the perplexities and ambiguities of language, power to 
detect identity of meaning under difference of expres- 
sion, a ready apprehension of all that a proposition 
implies, all that may be educed or deduced from it — 
whatever helps to these ends must be of perpetual use. 
" To purge the understanding of those errors which 
lie in the confusion and perplexities of an inconsequent 
thinking,'* is a modern description of the main scope 
of Logic.^ It is a good description of the branch of 
Logic that keeps closest to the Aristotelian tradition. 

1 Like every other fashion, Yes-and-No Dialectic had its period^ 
its rise and fall. The invention of it is ascribed to Zeno the 
Eleatic, the answering and questioning Zeno, who flourished 
about the middle of the fifth century B.C. Socrates (469-399) was 
in his prime at the beginning of the great Peloponnesian Wat 
when Pericles died in 429. In that year Plato was born, and 
lived to 347, " the olive groves of Academe " being the established 
centre of his teaching from about 386 onwards. Aristotle (384- 
322), who was the tutor of Alexander the Great, established his 
school at the Lyceum when Alexander became king in 336 and 
set out on his career of conquest. That Yes-and-No Dialectic was 
then a prominent exercise, his logical treatises everywhere bear 
witness. The subsequent history of the game is obscure. It is 
probable that Aristotle's thorough exposition of its legitimate 
arts and illegitimate tricks helped to destroy its interest as an 
amusement. 

' Hamilton's LectureSt iii. p. 37. 



IS Introduction. 

The limitations as well as the uses of Aristotle's logic 
may be traced to the circumstances of its origin. Both 
parties to the disputation, Questioner and Respondent 
alike, were mainly concerned with the inter-dependence 
of the propositions put forward. Once the Respondent 
had given his assent to a question, he was bound in 
consistency to all that it implied. He must take all 
the consequences of his admission. It might be true 
or it might be false as a matter of fact : all the same 
he was bound by it : its truth or falsehood was 
immaterial to his position as a disputant. On the 
other hand, the Questioner could not go beyond the 
admissions of the Respondent. It has often been 
alleged as a defect in the Syllogism that the conclusion 
does not go beyond the premisses, and ingenious 
attempts have been made to show that it is really an 
advance upon the premisses. But having regard to the 
primary use of the syllogism, this was no defect, but a 
necessary character of the relation. The Questioner 
could not in fairness assume more than had been 
granted by implication. His advance could only be an 
argumentative advance : if his conclusion contained a 
grain more than was contained in the premisses, it was 
a sophistical trick, and the Respondent could draw 
back and withhold his assent. He was bound in con- 
sistency to stand by his admissions; he was not 
bound to go a fraction of an inch beyond them. 

We thus see how vain it is to look to the Aristotelian 
tradition for an organon of truth or a criterion of 
falsehood. Directly and primarily, at least, it was not 
so ; the circumstances of its origin gave it a different 
bent. Indirectly and secondarily, no doubt, it served 
this purpose, inasmuch as truth was the aim of all 
serious thinkers who sought to clear their minds and 



The Origin and Scope of Logic. 13 

the minds of others by Dialectic. But in actual debate 
truth was represented merely by the common-sense of 
the audience. A dialectician who gained a triumph by 
outraging this, however cleverly he might outwit his 
antagonist, succeeded only in amusing his audience, 
and dialecticians of the graver sort aimed at more 
serious uses and a more respectful homage, and did 
their best to discountenance merely eristic disputation. 
Further, it would be a mistake to conclude because 
Aristotle's Logic, as an instrument of Dialectic, con- 
cerned itself with the syllogism of propositions rather 
than their truth, that it was merely an art of quibbling. 
On the contrary, it was essentially the art of preventing 
and exposing quibbling. It had its origin in quibbling, 
no doubt, inasmuch as what we should call verbal 
quibbling was of the essence of Yes-and-No Dialectic, 
and the main secret of its charm for an intellectual 
and disputatious people; but it came into being as 
a safeguard against quibbling, not a serviceable 
adjunct. 

\ The mediaeval developments of Logic retained and 
i even exaggerated the syllogistic character of the 
original treatises. Interrogative dialectic had disap- 
peared in the Middle Ages whether as a diversion 
or as a discipline : but errors of inconsistency still 
remained the errors against which principally educated 
men needed a safeguard. Men had to keep their 
utterances in harmony with the dogmas of the Church. 
A clear hold of the exact implications of a proposition, 
whether singly or in combination with other proposi- 
tions, was still an important practical need. The 
Inductive Syllogism was not required, and its treatment 
dwindled to insignificance in mediaeval text-books, but 



\ 



14 Introducti&n. 

the Deductive Syllogism and the formal apparatus 
for the definition of terms held the field. 

It was when observation of Nature and its laws 
became a paramount pursuit that the defects of 
Syllogistic Logic began to be felt. Errors against 
which this Logic offered no protection then called for 
a safeguard — especially the errors to which men are 
liable in the investigation of cause and effect. " Bring 
your thoughts into harmony one with another," was 
the demand of Aristotle's age. " Bring your thoughts 
into harmony with authority," was the demand of the 
Middle Ages. " Bring them into harmony with fact," 
was the requirement most keenly felt in more recent 
times. It is in response to this demand that what 
is commonly but not very happily known as Inductive 
Logic has been formulated. 

In obedience to custom, I shall follow the now 
ordinary division of Logic into Deductive and Indue 
tive. The titles are misleading in many ways, but 
they are fixed by a weight of usage which it would 
be vain to try to unsettle. Both come charging down 
the stream of time each with its cohort of doctrines 
behind it, borne forward with irresistible momentum. 

The best way of preventing confusion now is to 
retain the established titles, recognise that the doctrines 
behind each have a radically different aim or end, and 
supply the interpretation of this end from history. 
What they have in common may be described as the 
prevention of error, the organisation of reason against 
error. I have shown that owing to the bent impressed 
upon it by the circumstances of its origin, the errors 
chiefly safeguarded by the Aristotelian logic were the 
errors of inconsistency. The other branch of Logic, 
commonly called Induction, was really a separate 



The Origin and Scope of Logic. 15 

evolution, having its origin in a different practical 
need. The history of this I will trace separately 
after we have seen our way through the Aristotelian 
tradition and its accretions. The Experimental 
Methods are no less manifestly the germ, the evolu- 
tionary centre or starting-point, of the new Logic 
than the Syllogism is of the old, and the main errors 
safeguarded are errors of fact and inference from 
fact. 

At this stage it will be enough to indicate briefly 
the broad relations between Deductive Logic and 
Inductive Logic. 

Inductive Logic, as we now understand it — the Logic 
of Observation and Explanation — was first formulated 
and articulated to a System of Logic by J. S. Mill. It 
was he that added this wing to the old building. But 
the need of it was clearly expressed as early as the 
thirteenth century. Roger Bacon, the Franciscan friar 
(1214-1292), and not his more illustrious namesake 
Francis, Lord Verulam, was the real founder of 
Inductive Logic. It is remarkable that the same 
century saw Syllogistic Logic advanced to its most 
complete development in the system of Petrus 
Hispanus, a Portuguese scholar who under the title 
of John XXI. filled the Papal Chair for eight months 
in 1276-7. 

A casual remark of Roger Bacon's in the course of 
his advocacy of Experimental Science in the Opus 
Majus draws a clear line between the two branches 
of Logic. "There are," he says, *'two ways of 
knowing, by Argument and by Experience. Argument 
concludes a question, but it does not make us feel 
certain, unless the truth be also found in ex- 
perience.'' 



1 6 Introduction. 

On this basis the old Logic may be clearly distinguished 
from the new, taking as the general aim of Logic the 
protection of the mind against the errors to which it 
is liable in the acquisition of knowledge. 

All knowledge, broadly speaking, comes either from 
Authority, /.^., by argument from accepted premisses, 
or from Experience. If it comes from Authority it 
comes through the medium of words : if it comes from 
Experience it comes through the senses. In taking 
in knowledge through words we are liable to certain 
errors ; and in taking in knowledge through the senses 
we are liable to certain errors. To protect against the 
one is the main end of " Deductive *' Logic : to protect 
against the other is the main end of ** Inductive * 
Logic. As a matter of fact the pith of treatises on 
Deduction and Induction is directed to those enda 
respectively, the old meanings of Deduction and 
Induction as formal processes (to be explained after- 
wards) being virtually ignored. 

There is thus no antagonism whatever between the 
two branches of Logic. They are directed to different 
ends. The one is supplementary to the other. The 
one cannot supersede the other. 

Aristotelian Logic can never become superfluous as 
long as men are apt to be led astray by words. Its 
ultimate business is to safeguard in the interpretation 
of the tradition of language. The mere syllogistic, the 
bare forms of equivalent or consistent expression, have 
a very limited utility, as we shall see. But by cogent 
sequence syllogism leads to proposition, and proposition 
to term, and term to a close study of the relations 
between words and thoughts and things. 



Logic as a Preventive of J£rror or Fallacy, 17 

IL— LOGIC AS A PREVENTIVE OF ERROR OR 
FALLACY.—THE INNER SOPHIST. 

Why describe Logic as a system of defence against 
error ? Why say that its main end and aim is the 
organisation of reason against confusion and false- 
hood ? Why not rather say, as is now usual, that its 
end is the attainment of truth ? Does this not come 
to the same thing ? 

Substantially, the meaning is the same, but the 
latter expression is more misleading. To speak of 
Logic as a body of rules for the investigation of truth 
has misled people into supposing that Logic claims to 
be an art of Discovery, that it claims to lay down rules 
by simply observing which investigators may infallibly 
arrive at new truths. Now, this does not hold even of 
the Logic of Induction, still less of the older Logic, the 
precise relation of which to truth will become apparent 
as we proceed. It is only by keeping men from going 
astray and by disabusing them when they think they 
have reached their destination that Logic helps men 
on the road to truth. Truth often lies hid in the centre 
of a maze, and logical rules only help the searcher 
onwards by giving him warning when he is on the 
wrong track and must try another. It is the searcher's 
own impulse that carries him forward : Logic does not 
so much beckon him on to the right path as beckon 
him back from the wrong. In laying down the condi- 
tions of correct interpretation, of valid argument, of 
trustworthy evidence, of satisfactory explanation, 
Logic shows the inquirer how to test and purge his 
conclusions, not how to reach them. 

To discuss, as is sometimes done, whether Fallacies 
lie within the proper sphere of Logic, is to obscure the 

2 



t8 Introduction, 

real connexion between Fallacies and Logic. It is the 
existence of Fallacies that calls Logic into existence ; 
as a practical science Logic is needed as a protection 
against Fallacies. Such historically is its origin. We 
may, if we like, lay down an arbitrary rule that a 
treatise on Logic should be content to expound the 
correct forms of interpretation and reasoning and 
should not concern itself with the wrong. If we take 
this view we are bound to pronounce Fallacies extra- 
logical. But to do so is simply to cripple the useful- 
ness of Logic as a practical science. The manipulation 
of the bare logical forms, without reference to fallacious 
departures from them, is no better than a nursery 
exercise. Every correct form in Logic is laid down as 
ft safeguard against some erroneous form to which 
men are prone, whether in the interpretation of argu- 
ment or the interpretation of experience, and the 
statement and illustration of the typical forms of 
wrong procedure should accompany pari passu the 
exposition of the right procedure. 

In accordance with this principle, I shall deal with 
special fallacies, special snares or pitfalls — misappre- 
hension of words, misinterpretation of propositions, 
misunderstanding of arguments, misconstruction ol 
facts, evidences, or signs — each in connexion with its 
appropriate safeguard. This seems to me the most 
profitable method. But at this stage, it may be worth 
while, by way of emphasising the need for Logic as a 
science of rational belief, to take a survey of the most 
general tendencies to irrational belief, the chief kinds 
of illusion or bias that are rooted in the human consti- 
tution. We shall then better appreciate the magnitude 
of the task that Logic attempts in seeking to protect 



Logic as a Prevent fve of Error or Fallacy. 19 

reason against its own fallibility and the pressure of 
the various forces that would usurp its place. 

It is a common notion that we need Logic to pro- 
tect us against the arts of the Sophist, the dishonest 
juggler with words and specious facts. But in truth 
the Inner Sophist, whose instruments are our own 
inborn propensities to error, is a much more dangerous 
enemy. For once that we are the victims of designing 
Sophists, we are nine times the victims of our own 
irrational impulses and prejudices. Men generally 
deceive themselves before they deceive others. 

Francis Bacon drew attention to these inner per- 
verting influences, these universal sources of erroneous 
belief, in his De Augmentis and again in his Novum 
Organum, under the designation of Idola (ctScoXa), 
deceptive appearances of truth, illusions. His classi- 
fication of Idola — Idola Tribus^ illusions common to 
all men, illusions of the race ; Idola Specus, personal 
illusions, illusions peculiar to the " den " in which 
each man lives ; Idola Fori, illusions of conversation, 
vulgar prejudices embodied in words; Idola Theatric 
illusions of illustrious doctrine, illusions imposed by 
the dazzling authority of great names — is defective as 
a classification inasmuch as the first class includes all 
the others, but like all his writings it is full of sagacious 
remarks and happy examples. Not for the sake of 
novelty, but because it is well that matters so important 
should be presented from more than one point of view, 
I shall follow a division adapted from the more scien- 
tific, if less picturesque, arrangement of Professor 
Bain, in his chapter on the Fallacious Tendencies of 
the Human Mind.^ 

^ Bain's Logicy bk. vi. chap. iii. Bacon intended his Idola to 
beax the same relation to his Novum Organum that Aristotle's 



20 Introduction. 

The illusions to which we are all subject may best 
be classified according to their origin in the depths of 
our nature. Let us try to realise how illusory beliefs 
arise. 

What 18 a belief? One of the uses of Logic is 
to set us thinking about such simple terms. An 
exhaustive analysis and definition of belief is one 
of the most difficult of psychological problems. We 
cannot enter upon that : let us be content with a few 
simple characters of belief. 

First, then, belief is a state of mind. Second, this 
state of mind is outward-pointing : it has a reference 
beyond itself, a reference to the order of things outside 
us. In believing, we hold that the world as it is, has 
been, or will be, corresponds to our conceptions of 
it. Third, belief is the guide of action : it is in accord- 
ance with what we believe that we direct our activities. 
If we want to know what a man really believes, we 
look at his action. This at least is the clue to what 
he believes at the moment. " I cannot," a great 
orator once said, " read the minds of men.*' This was 
received with ironical cheers. " No,'* he retorted, " but 
I can construe their acts.*' Promoters of companies 
are expected to invest their own money as a guarantee 
of good faith. If a man says he believes the world is 
coming to an end in a year, and takes a lease of a 
house for fifteen years, we conclude that his belief is 
not of the highest degree of strength. 

Fallacies or Sophistical Tricks bore to the old Organum. But in 
truth, as I have already indicated, what Bacon classifies is our 
inbred tendencies to form idola or false images, and it is these 
same tendencies that make us liable to the fallacies named by 
Aristotle. Some of Aristotle's, as we shall see, are fallacies of 
Induction. 



Logic as a Preventive of Error or Fallacy, ai 

The close connexion of belief with our activities, 
enables us to understand how illusions, false concep- 
tions of reality, arise. The illusions of Feeling and 
the illusions of Custom are well understood, but other 
sources of illusion, which may be designated Impatient 
Impulse and Happy Exercise, are less generally 
recognised. An example or two will show what is 
meant. We cannot understand the strength of these 
perverting influences till we realise them in our own 
case. We detect them quickly enough in others. 
Seeing that in common speech the word illusion 
implies a degree of error amounting almost to insanity, 
and the illusions we speak of are such as no man is 
ever quite free from, it is perhaps less startling to use 
the word bias. 

The Bias of Impatient Impulse. 

As a being formed for action, not only does healthy 
man take a pleasure in action, physical and mental, for 
its own sake, irrespective of consequences, but he is so 
charged with energy that he cannot be comfortable 
unless it finds a free vent. In proportion to the amount 
and excitability of his energy, restraint, obstruction, 
delay is irksome, and soon becomes a positive and 
intolerable pain. Any bar or impediment that gives us 
pause is hateful even to think of : the mere prospect 
annoys and worries. 

Hence it arises that belief, a feeling of being pre- 
pared for action, a conviction that the way is clear 
before us for the free exercise of our activities, is a very 
powerful and exhilarating feeling, as much a necessity 
of happy existence as action itself We see this when 
we consider how depressing and uncomfortable a 



19 Introduction. 

condition is the opposite state to belief, namely, doubt, 
perplexity, hesitation, uncertainty as to our course. 
And realising this, we see how strong a bias we 
have in this fact of our nature, this imperious inward 
necessity for action ; how it urges us to act without 
regard to consequences, and to jump at beliefs without 
inquiry. For, unless inquiry itself is our business, a 
self- sufficient occupation, it means delay and obstruc- 
tion. 

This ultimate fact of our nature, this natural inbred 
constitutional impatience, explains more than half of 
the wrong beliefs that we form and persist in. We 
must have a belief of some kind : we cannot be happy 
till we get it, and we take up with the first that seems 
to show the way clear. It may be right or it may be 
wrong : it is not, of course, necessarily always wrong : 
but that, so far as we are concerned, is a matter ol 
accident. The pressing need for a belief of some sort, 
upon which our energies may proceed in anticipation 
at least, will not allow us to stop and inquire. Any 
course that offers a relief from doubt and hesitation, 
any conviction that lets the will go free, is eagerly 
embraced. 

It may be thought that this can apply only to beliefs 
concerning the consequences of our own personal 
actions, affairs in which we individually play a part. 
It is from them, no doubt, that our nature takes this 
set : but the habit once formed is extended to all sorts 
of matters in which we have no personal interest. Tell 
an ordinary Englishman, it has been wittily said, that 
it is a question whether the planets are inhabited, and 
he feels bound at once to have a confident opinion on 
the point. The strength of the conviction bears no 
proportion to the amount of reason spent in reaching 



Logic as a Preventive of Error or Fallacy. 23 

it, unless it may be said that as a general rule the less 
a belief is reasoned the more confidently it is held. 

"A grocer," writes Mr. Bagehot in an acute essay 
on ** The Emotion of Conviction," * ** has a full creed 
as to foreign policy, a young lady a complete theory 
of the Sacraments, as to which neither has any doubt. 
A girl in a country parsonage will be sure that Paris 
never can be taken, or that Bismarck is a wretch." An 
attitude of philosophic doubt, of suspended judgment, 
is repugnant to the natural man. Belief is an inde- 
pendent joy to him. 

This bias works in all men. While there is life, 
there is pressure from within on belief, tending to push 
reason aside. The force of the pressure, of course, 
varies with individual temperament, age, and other 
circumstances. The young are more credulous than 
the old, as having greater energy : they are apt, as 
Bacon puts it, to be ** carried away by the sanguina 
element in their temperament". Shakespeare's Laertea 
is a study of the impulsive temperament, boldly con- 
trasted with Hamlet, who has more discourse of reason. 
When Laertes hears that his father has been killed, he 
hurries home, collects a body of armed sympathisers, 
bursts into the presence of the king, and threatens with 
his vengeance — the wrong man. He never pauses to 
make inquiry : like Hotspur he is " a wasp-stung and 
impatient fool " ; he must wreak his revenge on 
somebody, and at once. Hamlet's father also has 
been murdered, but his reason must be satisfied before 
he proceeds to his revenge, and when doubtful proof is 
offered, he waits for proof more relative. 

Bacon's Idola Tribus and Dr. Bain's illustrations of 

^ Bagehot's Literary Studies, ii. 427. 



34 Tntroduction. 

incontinent energy, are mostly examples of unreasoning 
intellectual activity, hurried generalisations, unsound 
and superficial analogies, rash hypotheses. Bacon 
quotes the case of the sceptic in the temple of 
Poseidon, who, when shown the offerings of those 
who had made vows in danger and been delivered, 
and asked whether he did not now acknowledge the 
power of the god, replied : " But where are they who 
made vows and yet perished ? " This man answered 
rightly, says Bacon. In dreams, omens, retributions, 
and such like, we are apt to remember when they 
come true and to forget the cases when they fail. 
If we have seen but one man of a nation, we are 
apt to conclude that all hi^ countrymen are like him ; 
we cannot suspend our judgment till we have seen 
more. Confident belief, as Dr. Bain remarks, is the 
primitive attitude of the human mind : it is only by 
slow degrees that this is corrected by experience. 
The old adage, " Experience teaches fools," has a 
meaning of its own, but in one sense it is the reverse 
of the truth. The mark of a fool is that he is not 
taught by experience, and we are all more or less 
intractable pupils, till our energies begin to faiL 

The Bias of Happy Exercise. 

If an occupation is pleasant in itself, if it fully 
satisfies our inner craving for action, we are liable 
to be blinded thereby to its consequences. Happy 
exercise is the fool's Paradise. The fallacy lies not 
in being content with what provides a field for the 
full activity of our powers : to be content in such a 
case may be the height of wisdom : but the fallacy 
lies in claiming for our occupation results, benefits, 



Logic as a Preventive of Error or Fallacy. 25 

utilities that do not really attend upon it. Thus we 
see subjects of study, originally taken up for some 
purpose, practical, artistic, or religious, pursued into 
elaborate detail far beyond their original purpose, 
and the highest value, intellectual, spiritual, moral, 
claimed for them by their votaries, when in truth they 
merely serve to consume so much vacant energy, and 
may be a sheer waste of time that ought to be other- 
wise employed. 

But as I am in danger of myself furnishing an 
illustration of this bias — it is nowhere more prevalent 
than in philosophy — I will pass to our next head. 

The Bias of the Feelings, 

This source of illusion is much more generally 
understood. The blinding and perverting influence 
of passion on reason has been a favourite theme with 
moralists ever since man began to moralise, and is 
acknowledged in many a popular proverb. " Love is 
blind ; " " The wish is father to the thought ; " " Some 
people's geese are all swans ; '' and so forth. 

We need not dwell upon the illustration of it. Fear 
and Sloth magnify dangers and difficulties ; Affection 
can see no imperfection in its object : in the eyes of 
Jealousy a rival is a wretch. From the nature of the 
case we are much more apt to see examples in others 
than in ourselves. If the strength of this bias were 
properly understood by everybody, the mistake would 
not so often be committed of suspecting bad faith, 
conscious hypocrisy, when people are found practising 
the grossest inconsistencies, and shutting their eyes 
apparently in deliberate wilfulness to facts held under 
their very noses. Men are inclined to ascribe this 



26 Introduction. 

human weakness to women. Reasoning from feeling 
is said to be feminine logic. But it is a human 
weakness. 

To take one very powerful feeling, the feeling of 
self-love or self-interest — this operates in much more 
subtle ways than most people imagine, in ways so 
subtle that the self-deceiver, however honest, would 
fail to be conscious of the influence if it were pointed 
out to him. When the slothful man saith. There is a 
lion in the path, we can all detect the bias to his 
belief, and so we can when the slothful student says 
that he will work hard to-morrow, or next week, or 
next month ; or when the disappointed man shows an 
exaggerated sense of the advantages of a successful 
rival or of his own disadvantages. But self-interest 
works to bias belief in much less palpable ways than 
those. It is this bias that accounts for the difficulty 
that men of antagonistic interests have in seeing the 
arguments or believing in the honesty of theil 
opponents. You shall find conferences held between 
capitalists and workmen in which the two sides, both 
represented by men incapable of consciously dishonest 
action, fail altogether to see the force of each other's 
arguments, and are mutually astonished each at the 
other's blindness. 

The Bias of Custom. 

That custom, habits of thought and practice, affect 
belief, is also generally acknowledged, though the 
strength and wide reach of the bias is seldom realised. 
Very simple cases of unreasoning prejudice were 
adduced by Locke, who was the first to suggest a 
general explanation of them in the "Association of 



Logic as a Preventive of Error or Fallacy. 27 

Ideas** {Human Understanding^\!k. ii, ch, xxxiii.). There 
is, for instance, the fear that overcomes many people 
when alone in the dark. In vain reason tells them that 
there is no real danger ; they have a certain tremor of 
apprehension that they cannot get rid of, because 
darkness is inseparably connected in their minds with 
images of horror. Similarly we contract unreasonable 
dislikes to places where painful things have happened 
to us. Equally unreasoning, if not unreasonable, is 
our attachment to customary doctrines or practices, 
and our invincible antipathy to those who do not 
observe them. 

Words are very common vehicles for the currency 
of this kind of prejudice, good or bad meanings being 
attached to them by custom. The power of words in 
this way is recognised in the proverb : ** Give a dog 
a bad name, and then hang him". These verbal 
prejudices are Bacon's Idola Fori^ illusions of convex 
sation. Each of us is brought up in a certain sect ol 
party, and accustomed to respect or dishonour certain 
sectarian or party names, Whig, Tory, Radical, 
Socialist, Evolutionist, Broad, Low, or High Church. 
We may meet a man without knowing under what 
label he walks and be charmed with his company : 
meet him again when his name is known, and all is 
changed. 

Such errors are called Fallacies of Association to 
point to the psychological explanation. This is that 
by force of association certain ideas are brought into 
the mind, and that once they are there, we cannot help 
giving them objective reality. For example, a doctor 
comes to examine a patient, and finds certain 
symptoms. He has lately seen or heard of many cases 
of infiuenza^ we shall say ; influenza is running in his 



28 Introduction. 

head. The idea once suggested has all the advantage 
of possession. 

But why is it that a man cannot get rid of an idea ? 
Why does it force itself upon him as a belief ? Associa- 
tion, custom, explains how it got there, but not why it 
persists in staying. 

To explain this we must call in our first fallacious 
principle, the Impatience of Doubt or Delay, the 
imperative inward need for a belief of some sort. 

And this leads to another remark, that though for 
convenience of exposition, we separate these various 
influences, they are not separated m practice. They 
may and often do act all together, the Inner Sophist 
concentrating his forces. 

Finally, it may be asked whether, seeing that 
illusions are the offspring of such highly respectable 
qualities as excess of energy, excess of feeling, excess 
of docility, it is a good thing for man to be disillu- 
sioned. The rose-colour that lies over the world for 
youth is projected from the abundant energy and 
feeling within : disillusion comes with failing energies, 
when hope is " unwilling to be fed ". Is it good then 
to be disillusioned ? The foregoing exposition would 
be egregiously wrong if the majority of mankind did 
not resent the intrusion of Reason and its organising 
lieutenant Logic. But really there is no danger that 
this intrusion succeeds to the extent of paralysing 
action and destroying feeling, and uprooting custom. 
The utmost that Logic can do is to modify the excess 
of these good qualities by setting forth the conditions 
of rational belief. The student who masters those 
conditions will soon see the practical wisdom of 
applying his knowledge only in cases where the 
grounds of rational belief are within his reach. To 



The Axioms of Dialectic and of Syllogism. 29 

apply it to the consequences of every action would be 
to yield to that bias of incontinent activity which is, 
perhaps, our most fruitful source of error. 



III.— THE AXIOMS OF DIALECTIC AND OF 
SYLLOGISM. 

There are certain principles known as the Laws of 
Thought or the Maxims of Consistency. They are 
variously expressed, variously demonstrated, and 
variously interpreted, but in one form or another they 
are often said to be the foundation of all Logic. It 
is even said that all the doctrines of Deductive or 
Syllogistic Logic may be educed from them. Let us 
take the most abstract expression of them, and see 
how they originated. Three laws are commonly 
given, named respectively the Law of Identity, the 
Law of Contradiction and the Law of Excluded 
Middle. 

1. The Law of Identity. A is A. Socrates is 
Socrates. Guilt is guilt. 

2. The Law of Contradiction. A is not not-A. 
Socrates is not other than Socrates. Guilt is not 
other than guilt. Or A is not at once b and not-^. 
Socrates is not at once good and not-good. Guilt is 
not at once punishable and not-punishable. 

3. The Law of Excluded Middle. Everything is 
either A or not-A ; or, A is either b or not-^. A given 
thing is either Socrates or not-Socrates, either guilty 
or not-guilty. It must be one or the other: no middle 
is possible. 

Why lay down principles so obvious, in some inter- 
pretations, and so manifestly sophistical in others ? 
The bare forms of modern Logic have been reached 



30 Introduction^ 

by a process of attenuation from a passage in Aristotle's 
Metaphysics'^ (iii. 3, 4, 1005^^ - 1008). He is there 
laying down the first principle of demonstration, which 
he takes to be that " it is impossible that the same 
predicate can both belong, and not belong, to the same 
subject, at the same time, and in the same sense '*.' 
That Socrates knows grammar, and does not know 
grammar — these two propositions cannot both be 
true at the same time, and in the same sense. Two 
contraries cannot exist together in the same subject. 
The double answer Yes and No cannot be given to one 
and the same question understood in the same sense. 

But why did Aristotle consider it necessary to lay 
down a principle so obvious ? Simply because among 
the subtle dialecticians who preceded him the principle 
had been challenged. The Platonic dialogue Euthy- 
demus shows the farcical lengths to which such 
quibbling was carried. The two brothers vanquish 
all opponents, but it is by claiming that the answer 
No does not preclude the answer Yes. " Is not the 
honourable honourable, and the base base ? " asks 
Socrates. " That is as I please," replies Dionyso- 
dorus. Socrates concludes that there is no arguing 
with such men : they repudiate the first principles of 
dialectic. 

There were, however, more respectable practitioners 

^ The first statement of the Law of Identity in the form Eni 
est ens is ascribed by Hamilton {Lectures, iii. 91) to Antonius 
Andreas, a fourteenth century commentator on the Metaphysics, 
But Andreas is merely expounding what Aristotle sets forth in 
iii. 4, 1006 a, b. Ens est ens does not mean in Andreas what 
A is A means in Hamilton. 

* rh yhp ahrh afia tnrdpx^ty T€ koI fi^ {nrdpx^^v hZvvarov r^ avrf 
Koi Kara rh avrh, . , , aVrrf 5^ iratrwv iiTTl ^e^aioTwni rwv apx^ov. 
iii. 3, 10056, 19-23. 



T%e Axoims of Dialectic and of Syllogism, 31 

who canvassed on more plausible grounds any form 
into which ultimate doctrines about contraries and 
contradictions, truth and falsehood, could be put, and 
therefore Aristotle considered it necessary to put forth 
an d defend at elaborate length a statement of a first 
principle of demonstration. ** Contradictions cannot 
both be true of the same subject at the same time 
and in the same sense." This is the original form of 
the Law of Contradiction. 

The words " of the same subject," " at the same 
time," and " in the same sense," are carefully chosen 
to guard against possible quibbles. ** Socrates knows 
grammar'' By Socrates we must mean the same 
individual man. And even of the same man the 
assertion may be true at one time and not at another. 
There was a time when Socrates did not know 
grammar, though he knows it now. And the assertion 
may be true in one sense and not in another. It may 
be true that Socrates knows grammar, yet not that he 
knows everything that is to be known about grammar, 
or that he knows as much as Aristarchus. 

Aristotle acknowledges that this first principle 
cannot itself be demonstrated, that is, deduced from 
any other. If it is denied, you can only reduce the 
denier to an absurdity. And in showing how to 
proceed in so doing, he says you must begin by 
coming to an agreement about the words used, that 
they signify the same for one and the other disputant.^ 

1 Hamilton credits Andreas with maintaining, " against Aris- 
totle," that "the principle of Identity, and not the principle of 
Contradiction, is the one absolutely first '\ Which comes first, is 
a scholastic question on which ingenuity may be exercised. But 
in fact Aristotle put the principle of Identity first in the above 
plain sense, and Andreas only expounded more formally what 
Aristotle had said. 



32 Introduction. 

No dialectic is possible without this understanding. 
This first principle of Dialectic is the original of the 
Law of Identity. While any question as to the 
truth or falsehood of a question is pending, from the 
beginning to the end of any logical process, the words 
must continue to be accepted in the same sense. 
Words must have an identical reference to things. 

Incidentally in discussing the Axiom of Contradiction 
{aiiwfjia TTJq dvTK^ao-ccDs),^ Aristotle lays down what is now 
known as the Law of Excluded Middle. Of two con- 
tradictories one or other must be true : we must either 
affirm or deny any one thing of any other : no mean 
or middle is possible. 

In their origin, then, these so-called Laws of Thought 
were simply the first principles of Dialectic and 
Demonstration. Consecutive argument, coherent 
ratiocination, is impossible unless they are taken fof 
granted. 

If we divorce or abstract them from their original 
application, and consider them merely as laws o\ 
thinking or of being, any abstract expression, or 
illustration, or designation of them may easily be 
pushed into antagonism with other plain truths or 
first principles equally rudimentary. Without entering 
into the perplexing and voluminous discussion to 
which these laws have been subjected by logicians 
within the last hundred years, a little casuistry is 
necessary to enable the student to understand within 
what limits they hold good. 

Socrates is Socrates. The name Socrates is a name 

ktofdyai ty kuO' tphs dnovv, Metaph. iii. 7, 10 116, 23-4. 



The Axioms of Dialectic and of Syllogism. 33 

for something to which you and I refer when we 
use the name. Unless we have the same reference, 
we cannot hold any argument about the thing, or 
make any communication one to another about it. 

But if we take Socrates is Socrates to mean that, "An 
object of thought or thing is identical with itself," *'An 
object of thought or thing cannot be other than itself," 
and call this a law of thought, we are met at once by 
a difficulty. Thought, properly speaking, does not 
begin till we pass beyond the identity of an object 
with itself. Thought begins only when we recognise 
the likeness between one object and others. To keep 
within the self-identity of the object is to suspend 
thought. "Socrates was a native of Attica," 
" Socrates was a wise man," " Socrates was put to 
death as a troubler of the commonweal " — whenever 
we begin to think or say anything about Socrates, to 
ascribe any attributes to him, we pass out of his self- 
identity into his relations of likeness with other men, 
into what he has in common with other men. 

Hegelians express this plain truth with paradoxical 
point when they say : " Of any definite existence 
or thought, therefore, it may be said with quite 
as m.uch truth that it is noty as that it w, its own 
bare self ".^ Or, " A thing must other itself in order 
to be itself". Controversialists treat this as a sub- 
version of the laws of Identity and Contradiction. 
But it is only Hegel's fun — his paradoxical way of 
putting the plain truth that any object has more in 
common with other objects than it has peculiar to 
itself. Till we enter into those aspects of agreement 
with other objects, we cannot truly be said to think at 

* Prof. Caird*s Hegely p. 138. 
3 



34 Introduction, 

all. If we say merely that a thing is itself, we may 
as well say nothing about it. To lay down this is not 
to subvert the Law of Identity, but to keep it from 
being pushed to the extreme of appearing to deny the 
Law of Likeness, which is the foundation of all the 
characters, attributes, or qualities of things in our 
thoughts. 

That self-same objects are like other self-same 
objects, is an assumption distinct from the Law of 
Identity, and any interpretation of it that excludes 
this assumption is to be repudiated. But does not 
the law of Identity as well as the law of the likeness 
of mutually exclusive identities presuppose that there 
are objects self-same, like others, and different from 
others ? Certainly : this is one of the presuppositions 
of Logic.^ We assume that the world of which we 
talk and reason is separated into such objects in our 
vhoughts. We assume that such words as Socrates 
represent individual objects with a self-same being or 
substance ; that such words as wisdom^ humour^ ugliness^ 
runnings sittingy here^ thert^ represent attributes, quali- 
ties, characters or predicates of individuals ; that 
such words as man represent groups or classes of 
individuals. 

Some logicians in expressing the Law of Identity 
have their eye specially upon the objects signified 
by general names or abstract names, man^ education} 
** A concept is identical with the sum of its characters," 
or, " Classes are identical with the sum of the indi- 
viduals composing them". The assumptions thus 
expressed in technical language which will hereafter 

^See Venn, Empirical Logic, i-8. 

' E.g,y Hamilton, lect. v. ; Veitch's Institutes of Logic, chaps, 
^ii., xiU, 



The Axioms of Dialecttc and of Syllogism. 35 

be explained are undoubtedly assumptions that Logic 
makes : but since they are statements of the internal 
constitution of some of the identities that words repre- 
sent, to call them the Law of Identity is to depart 
confusingly from traditional usage.* 

That throughout any logical process a word must 
signify the same object, is one proposition : that the 
object signified by a general name is identical with 
the sum of the individuals to each of whom it is 
applicable, or with the sum of the characters that 
they bear in common, is another proposition. Logic 
assumes both : Aristotle assumed both : but it is the 
first that is historically the original of all expressions 
of the Law of Identity in modern text-books. 

Yet another expression of a Law of Identity which 
is really distinct from and an addition to Aristotle's 
original. Socrates was an Athenian, a philosopher^ an 
ugly man, an acute dialectician, etc. Let it be granted 
that the word Socrates bears the same signification 
throughout all these and any number more of predi- 
cates, we may still ask : " But what is it that Socrates 
signifies ? " The title Law of Identity is sometimes 
given ^ to a theory on this point. Socrates is Socrates, 
** An individual is the identity running through the 
totality of its attributes," Is this not, it may be 

1 The confusion probably arises in this way. First, these 
" laws " are formulated as laws of thought that Logic assumes. 
Second, a notion arises that these laws are the only postulates of 
Logic: that all logical doctrines can be "evolved" from them. 
Third, when it is felt that more than the identical reference of 
words or the identity of a thing with itself must be assumed in 
Logic, the Law of Identity is extended to cover this further 
assumption. 

* E,g., Bosanquet's Logic^ ii, 207. 



36 Introduction. 

asked, to confuse thought and being, to resolve 
Socrates into a string of words ? No : real existence 
is one of the admissible predicates of Socrates : one 
of the attributes under which we conceive him. But 
whether we accept or reject this " Law of Identity," 
it is an addition to Aristotle's dialectical ** law of 
identity " ; it is a theory of the metaphysical nature 
of the identity signified by a Singular name. And 
the same may be said of yet another theory of Identity, 
that, ** An individual is identical with the totality of its 
predicates," or (another way of putting the same theory), 
" An individual is a conflux of generalities ". 

To turn next to the Laws of Contradiction and 
Excluded Middle. These also may be subjected to 
Casuistry, making clearer what they assert by showing 
what they do not deny. 

They do not deny that things change, and that suc- 
cessive states of the same thing may pass into one 
another by imperceptible degrees. A thing may be 
neither here nor there : it may be on the passage 
from here to there : and, while it is in motion, we 
may say, with equal truth, that it is neither here nor 
there, or that it is both here and there. Youth passes 
gradually into age, day into night : a given man or a 
given moment may be on the borderland between the 
two. 

Logic does not deny the existence of indeterminate 
margins: it merely lays down that for purposes of 
clear communication and coherent reasoning the line 
must be drawn somewhere between ^, and not-^. 

A difference, however, must be recognised between 
logical negation and the negations of common thought 
and common speech. The latter are definite to a 



The Axioms of Dialectic and of Syllogism, 37 

degree with which the mere Logic of Consistency does 
not concern itself. To realise this is to understand 
more clearly the limitations of Formal Logic. 

In common speech, to deny a quality of anything is 
by implication to attribute to it some other quality of 
the same kind. Let any man tell me that " the streets 
of such and such a town are not paved with wood," I 
at once conclude that they are paved with some other 
material. It is the legitimate eff<5Ct of his negative 
proposition to convey this impression to my mind. If, 
proceeding on this, I go on to ask : " Then they are 
paved with granite or asphalt, or this or that ? " and 
he turns round and says : " I did not say they were 
paved at all," I should be justified in accusing him of 
a quibble. In ordinary speech, to deny one kind of 
pavement is to assert pavement of some kind. Simi- 
larly, to deny that So-and-so is not in the Twenty- 
first Regiment, is to imply that he is in another 
regiment, that he is in the army in some regiment. 
To retort upon this inference : " He is not in the 
army at all," is a quibble : as much so as it would be 
to retort : " There is no such person in existence ". 

Now Logic does not take account of this implication, 
and nothing has contributed more to bring upon it the 
reproach of quibbling. In Logic, to deny a quality is 
simply to declare a repugnance between it and the 
subject ; negation is mere sublation, taking away, and 
implies nothing more. Not-^ is entirely indefinite : 
it may cover anything except b. 

Is Logic then really useless, or even misleading, 
inasmuch as it ignores the definite implication of 
negatives in ordinary thought and speech ? In ignor- 
ing this implication, does Logic oppose this implication 
as erroneous ? Does Logic shelter the quibbler who 



38 Introducmn. 

trades upon it ? By no means : to jump to this con- 
clusion were a misunderstanding. The fact only is 
that nothing beyond the logical Law of Contradiction 
needs to be assumed for any of the processes of Formal 
Logic. Aristotle required to assume nothing more for 
his syllogistic formulae, and Logic has not yet included 
in its scope any process that requires any further 
assumption. " If not-^ represent everything except b, 
everything outside b, then that A is b, and that A is 
not-^, cannot both be true, and one or other of them 
must be true." 

Whether the scope of Logic ought to be extended is 
another question. It seems to me that the scope of 
Logic may legitimately be extended so as to take 
account both of the positive implication of negative!^ 
and the negative implication of positives. I therefore 
deal with this subject in a separate chapter following 
on the ordinary doctrines of Immediate Inference, 
where I try to explain the simple Law of Thought 
involved. When I say that the extension is legitimate^ 
I mean that it may be made without departing from 
the traditional view of Logic as a practical science, 
conversant with the nature of thought and its expression 
only in so far as it can provide practical guidance 
against erroneous interpretations and inferences. The 
extension that I propose is in effect an attempt to bring 
within the fold of Practical Logic some of the results 
of the dialectic of Hegel and his followers, such as Mr. 
Bradley and Mr. Bosanquet, Professor Caird and Pro- 
fessor Wallace.* 

The logical processes formulated by Aristotle are 

^Bradley, Prineifles of Logic; Bosanquet, Logic or The 
Morphology of Knowledge ; Caird, Hegel (in Blackwood's 
Philoiophical Classics) ; Wallace, The Logic of Hegel, 



The Axioms of DiaUcttc and of Syllogism. 39 

merely stages in the movement of thought towards 
attaining definite conceptions of reality. To treat 
their conclusions as positions in which thought may 
dwell and rest, is an error, against which Logic itself 
as a practical science may fairly be called upon to 
guard. It may even be conceded that the Aristotelian 
processes are artificial stages, courses that thought 
does not take naturally, but into which it has to be 
forced for a purpose. To concede this is not to con- 
cede that the Aristotelian logic is useless, as long as 
we have reason on our side in holding that thought is 
benefited and strengthened against certain errors by 
passing through those artificial stages. 



BOOK L 

THE LOGIC OF CONSISTENCY. SYLLOGISM AND 
DEFINITION. 



PART I 

THE ELEMENTS OF PROPOSITIONS, 

Chapter L 

GENERAL NAMES AND ALLIED DISTINCTIONS. 

To discipline us against the errors we are liable to 
in receiving knowledge through the medium o/ 
words — such is one of the objects of Logic, the 
main object of what may be called the Logic of 
Consistency. 

Strictly speaking, we may receive knowledge about 
things through signs or single words, as a nod, a wink, 
a cry, a call, a command. But an assertory sentence, 
proposition, or predication, is the unit with which Logic 
concerns itself — a sentence in which a subject is named 
and something is said or predicated about it. Let a 
man once understand the errors incident to this regular 
mode of communication, and he may safely be left to 
protect himself against the errors incident to more 
rudimentary modes. 

A proposition, whether long or short, is a unit, but 
it is an analysable unit. And the key to syllogistic 

(43) 



44 The Elements of Propositions. 

analysis is the General Name. Every proposition, 
every sentence in which we convey knowledge to 
another, contains a general name or its equivalent. 
That is to say, every proposition may be resolved 
into a form in which the predicate is a general name. 
A knowledge of the function of this element of speech 
is the basis of all logical discipline. Therefore, though 
we must always remember that the proposition is 
the real unit of speech, and the general name 
only an annlytic element, we take the general name 
and its alliod distinctions in thought and reality 
first. 

How propositions are analysed for syllogistic 
purposes will be shown by-and-by, but we must 
first explain various technical terms that logicians 
have devised to define the features of this cardinal 
element. The technical terms Class, Concept, 
Notion, Attribute, Extension or Denotation, 
Intension or Connotation, Genus, Species, Differ- 
entia, Singular Name, Collective Name, Abstract 
Name, all centre round it. 

A general name is a name applicable to a number 
of different things on the ground of some likeness 
among them, as man^ ratepayer^ man of courage^ 
man who fought at Wate^'loo. 

From the examples it will be seen that a general 
name logically is not necessarily a single word. Any 
word or combination of words that serves a certain 
function is technically a general name. The different 
ways of making in common speech the equivalent of 
a general name logically are for the grammarian to 
consider. 

In the definition of a general name attention is called 
to two distinct considerations, the individual objects to 



General Names and Allied Distinctions, 45 

each of which the name is applicable, and the points of 
resemblance among them, in virtue of which they have 
a common name. For those distinctions there are 
technical terms. 

Class is the technical term for the objects, different 
yet agreeing, to each of which a general name may be 
applied. 

The points of resemblance are called the common 
attributes of the class. 

A class may be constituted on one attribute or on 
several. Ratepayer^ woman ratepayer^ unmarried woman 
ratepayer: soldier ^ British soldier^ British soldier on 
foreign service. But every individual to which the 
general name can be applied must possess the common 
attribute or attributes. 

These common attributes are also called the Notion 
of the class, inasmuch as it is these that the mind 
notes or should note when the general name is applied 
Concept is a synonym perhaps in more common use 
than notion ; the rationale of this term (derived from 
con and capere^ to take or grasp together) being that it 
is by means of the points of resemblance that the 
individuals are grasped or held together by the mind. 
These common points are the one in the many, the 
same amidst the different, the identity signified by the 
common name. The name of an attribute as thought 
of by itself without reference to any individual or class 
possessing it, is called an Abstract name. By con- 
tradistinction, the name of an individual or a class is 
Concrete. 

Technical terms are wanted also to express the 
relation of the individuals and the attributes to the 
general name. The individuals jointly are spoken of 
as the Denotation, or Extension or Scope of the 



46 The Elements of Propositions^ 

name ; the common attributes as its Connotation, 
Intension, Comprehension, or Ground. The whole 
denotation, etc., is the class ; the whole connotation, 
etc., is the concept.* 



1 It has been somewhat too hastily assumed on the authority 
of Mansel (Note to Aldrich, pp. i6, 17) that Mill inverted the 
scholastic tradition in his use of the word Connotative, Mansel 
puts his statement doubtfully, and admits that there was some 
licence in the use of the word Connotative, but holds that in 
Scholastic Logic an adjective was said to ** signify primarily the 
attribute, and to connote or signify secondarily {Trpoa-a-rnnaiveiv) the 
subject of inhesion". The truth is that Mansel's view was a 
theory of usage not a statement of actual usage, and he had good 
feason for putting it doubtfully. 

As a matter of fact, the history of the distinction follows the 
simple type of increasing precision and complexity, and Mill was 
in strict accord with standard tradition. By the Nominalist 
commentators on the Summulce of Petrus Hispanus certain names, 
adjectives grammatically, are called Connotativa as opposed to 
Ahsolutay simply because they have a double function. White is 
connotative as signifying both a subject, such as Socrates, of 
whom "whiteness" is an attribute, and an attribute "whiteness": 
the names " Socrates " and " whiteness " are Absolute, as having 
but a single signification. Occam himself speaks of the subject 
as the primary signification, and the attribute as the secondary, 
because the answer to "What is white?" is " Something informed 
with whiteness," and the subject is in the nominative case while 
the attribute is in an oblique case (Logic, part i. chap. x.). Later 
on we find that Tataretus (Expositio in Summulas, a.d. 1501), 
while mentioning (Tract. Sept. De Appellationibus) that it is a 
matter of dispute among Doctores whether a connotative name 
connotat the subject or the attribute, is perfectly explicit in his 
own definition, " Terminus connotativus est qui praeter illud pro 
quo supponit connotat aliquid adjacere vel non adjacere rei pro 
qua supponit" (Tract. Sept. De Suppositionibus), And this 
remained the standard usage as long as the distinction remained 
in logical text-books. We find it very clearly expressed by 
Clichtoveus, a Nominalist, quoted as an authority by Guthutius 



General Names and Allied Distinctions, 47 

The limits of a " class " in Logic are fixed by the 
common attributes. Any individual object that 

in his Gymnasium Speculativum, Paris, 1607 {De Terminorum 
Cognitioney pp. 78-9). " Terminus absolutus est, qui solum illud 
pro quo in propositione supponit, significat. Connotativus autem, 
qui ultra idipsum, aliud importat.*' Thus man and animal are 
absolute terms, which simply stand for (supponunt pro) the things 
they signify. White is a connotative name, because " it stands 
for (supponit pro) a subject in which it is an accident : and beyond 
this, still signifies an accident, which is in that subject, and is 
expressed by an abstract name ". Only Clichtoveus drops the 
verb connotate perhaps as a disputable term, and says simply ultra 
xmportat. 

So in the Port Royal Logic (1662), from which possibly Mill 
took the distinction : " Les noms qui signifient les choses comme 
modifiees, marquant premi^rement et directement la chose, quoi- 
que plus confusement, et indirectement le mode, quoique plus 
distinctement, sont appeles adjectifs ou connotatifs ; comme rond, 
dur, juste, prudent" (part i. chap. ii.). 

What Mill did was not to invert Scholastic usage but to revive 
the distinction, and extend the word connotative to general names 
on the ground that they also imported the possession of attributes. 
The word has been as fruitful of meticulous discussion as it was 
in the Renaissance of Logic, though the ground has changed. 
The point of Mill's innovation was, premising that general names 
are not absolute but are applied in virtue of a meaning, to put 
emphasis on this meaning as the cardinal consideration. What 
he called the connotation had dropped out of sight as not being 
required in the Syllogistic Forms. This was as it were the point 
at which he put in his horn toltoss the prevalent conception of 
Logic as Syllogistic. 

The real drift of Mill's innovation has been obscured by the 
fact that it was introduced among the preliminaries of Syllogism, 
whereas its real usefulness and significance belongs not to 
Syllogism in the strict sense but to Definition. He added to 
the confusion by trying to devise forms of Syllogism based on 
connotation, and by discussing the Axiom of the Syllogism from 
this point of view. For syllogistic purposes, as we shall see, 
Aristotle's forms are perfect, and his conception of the proposition 



48 The Elements of Propositians. 

possesses these is a member. The statement of them 
is the Definition. 

To predicate a general name of any object, as, 
"This is a cat,** **This is a very sad affair," is to 
refer that object to a class, which is equivalent to 
saying that it has certain features of resemblance with 
other objects, that it reminds us of them by its likeness 
to them. Thus to say that the predicate of every 
proposition is a general name, expressed or implied, is 
the same as to say that every predication may be 
taken as a reference to a class. 

Ordinarily our notion or concept of the common 
features signified by general names is vague and hazy. 
The business of Logic is to make *"hem clear. It is to 
this end that the individual objects of the class are 



in extension the only correct conception. Whether the centre 
of gravity in Consistency Logic should not be shifted back 
from Syllogism to Definition, the latter being the true centre 
of consistency, is another question. The tendency of Mill's 
polemic was to make this change. And possibly the secret of 
the support it has recently received from Mr. Bradley and Mr. 
Bosanquet is that they, following Hegel, are moving in the 
same direction. 

In effect, MilPs doctrine of Connotation helped to fix a con- 
ception of the general name first dimly suggested by Aristotle 
when he recognised that names of genera and species signify 
Quality, in showing what sort a thing is. Occam carried this a 
step farther towards clear light by including among Connotative 
Terms such general names as " monk," names of classes that at 
once suggest a definite attribute. The third step was made by 
Mill in extending the term Connotation to such words as " man," 
" horse," the Infima Species of the Schoolmen, the Species of 
modern science. 

Whether connotation was the best term to use for this purpose, 
rather than extension, may be questioned : but at least it was in 
the line of tradition through Occam. 



^neral Names and Allied Distinctions. 49 

summoned before the mind. In ordinary thinking 
there is no definite array or muster of objects : when 
we think of "dog" or "cat," "accident," "book," 
"beggar," "ratepayer," we do not stop to call before 
the mind a host of representatives of the class, nor do 
we take precise account of their common attributes. 
The concept of " house " is what all houses have in 
common. To make this explicit would be no easy 
matter, and yet we are constantly referring objects to 
the class "house". We shall see presently that if 
we wish to make the connotation or concept clear we 
must run over the denotation or class, that is to say, 
the objects to which the general name is applied in 
common usage. Try, for example, to conceive clearly 
what is meant by house, tree, dog, walking-stick. 
You think of individual objects, so-called, and of what 
they have in common. 

A class may be constituted on one property or on 
many. There are several points common to all 
houses, enclosing walls, a roof, a means of exit and 
entrance. For the full concept of the natural kinds, 
meuy dogs, mice, etc., we should have to go to the 
natural historian. 

Degrees of generality. One class is said to be of 
higher generality than another when it includes that 
other and more. Thus animal includes man, dog, 
horse, etc. ; man includes Aryan, Semite, etc. ; Aryan 
includes Hindoo, Teuton, Celt, etc. 

The technical names for higher and lower classes 
are Genus and Species. These terms are not fixed as 
in Natural History to certain grades, but are purely 
relative one to another, and movable up and down a 
scale of generality. A class may be a species 
relatively to one clasS| which is above it, and a genus 

4 



50 The Elements of Propositions. 

relatively to one below it. Thus Aryan is a species 
of the genus man, Teuton a species of the genus 
Aryan. 

In the graded divisions of Natural History genus 
and species are fixed names for certain grades. Thus : 
Vertebrates form a " division " ; the next subdivision, 
e.g.^ Mammals, Birds, Reptiles, etc., is called a " class''; 
the next, e.g.^ Rodents, Carnivora, Ruminants, an 
"order"; the next, e,g,, Rats, Squirrels, Beavers, a 
•* genus " ; the next, e.g,j Brown rats, Mice, a 
"species". 

Vertebrates (division). 
Mammals, Birds, Reptiles, etc. (class). 
Rodents, Ruminants, Carnivors, etc. (order). 
Rats, Squirrels, Beavers, etc. (genus). 
Brown rats. Mice, etc. (species). 

If we subdivide a large class into smaller classes, 
and, again, subdivide these subdivisions, we come at 
last to single objects. 

Men« 



Europeans, Asiatics, etc, 

_j 

Eaglishmen, Frenchmen, etc. 



John Doe, Richard Roe, etc. 



General Names and Allied Distinctions, 



51 



A table of higher and lower classes arranged in order 
has been known from of old as a tree of division or 
classification. The following is Porphyry^s ** tree " : — 

Being 



Corporeal 



Incorporeal 



Animate 



Inanimate 



Sensible 



I 



Rational 




Insensible 



Irrational 



(Man) 



Socrates, Plato, and other individuals. 



5» The Elements of Propostifons. 

The single objects are called IndiYiduals, because 
the division cannot be carried farther. The highest 
class is technically the Summum Genus, or Genus 
generalissimum ; the next highest class to any species 
is the Proximum Genus ; the lowest group before you 
descend to individuals is the Infima Species, or Species 
specialissima. 

The attribute or attributes whereby a species is 
distinguished from other species of the same genus, is 
called its differentia or differentisa. The various 
species of houses are differentiated by their several 
uses, dwelling-house, town-house, ware-house, public- 
house. Poetry is a species of Fine Art, its differentia 
being the use of metrical language as its instrument. 

A lower class, indicated by the name of its higher 
class qualified by adjectives or adjective phrases 
expressing its differential property or properties, is said 
to be described per genus at differentiam. Examples : 
" Black-bird," ** note-book," ** clever man," " man of 
Kent," " eminent British painter of marine subjects ". 
By giving a combination of attributes common to him 
with nobody else, we may narrow down the application 
of a name to an individual : " The Commander-in- 
Chief of the British forces at the battle of Waterloo ". 

Other attributes of classes as divided and defined, 
have received technical names. 

An attribute common to all the individuals of a 
class, found in that class only, and following from the 
essential or defining attributes, though not included 
among them, is called a Proprium. 

An attribute that belongs to some, but not to all, or 
that belongs to all, but is not a necessary consequence 
of the essential attributes, is called an Aooident. 

The clearest examples of Propria are found in 



General Names and Allied Distinciicns. 53 

mathematical figures. Thus, the defining property of 
an equilateral triangle is the equality of the sides : the 
equality of the angles is a proprium. That the three 
angles of a triangle are together equal to two right 
angles is a proprium, true of all triangles, and deducible 
from the essential properties of a triangle. 

Outside Mathematics, it is not easy to find propria 
that satisfy the three conditions of the definition. It 
is a useful exercise of the wits to try for such. Edu- 
cability — an example of the proprium in mediaeval 
text-books — is common to men, and results from man's 
essential constitution ; but it is not peculiar ; other 
animals are educable. That man cooks his food \% 
probably a genuine proprium. 

That horses run wild in Thibet : that gold is found 
in California: that clergymen wear white ties, are 
examples of Accidents. Learning is an accident in 
man, though educability is a proprium. 

What is known technically as an Inseparable 
Accident, such as the black colour of the crow or the 
Ethiopian, is not easy to distinguish from the Pro- 
prium. It is distinguished only by the third character, 
deducibility from the essence.^ 

1 The history of the definition of the Proprium is an example of 
the tendency of distinctions to become more minute and at the 
same time more purposeless. Aristotle*s tSiov was an attribute, 
such as the laugh of the man or the bark of the dog, common to 
all of a class and peculiar to the class {quod convenit omni soli et 
semper) yet not comprised in the definition of the class. Porphyry 
recognised three varieties of t^ia besides this, four in all, as 
follows : — (i) an attribute peculiar to a species but not possessed 
by all, as knowledge of medicine or geometry ; (2) possessed by a 
whole species but not peculiar to it, as being a biped in man ; (3) 
peculiar to a species, and possessed by all at a certain time, as 
turning grey in old age ; (4) Aristotle's '* proprium,'* peculiar and 



54 The Elements of Propositions. 

Accidents that are both common and peculiar are often 
useful for distinguishing members of a class. Distinc- 
tive dresses or badges, such as the gown of a student, 
the hood of a D.D., are accidents, but mark the class of 
the individual wearer. So with the colours of flowers. 

GenuSy Species^ Differentia^ Propriuniy and Accidens 
have been known since the time of Porphyry as the 
Five Predicables. They are really only terms used 
in dividing and defining. We shall return to them 
and endeavour to show that they have no significance 
except with reference to fixed schemes, scientific or 
popular, of Division or Classification. 

Given such a fixed scheme, very nice questions 
may be raised as to whether a particular attribute is 
a defining attribute, or a proprium, or an accident, ot 
an inseparable accident. Such questions afford great 
scope for the exercise of the analytic intellect. 

We shall deal more particularly with degrees of 
generality when we come to Definition. This much 
has been necessary to explain an unimportant but 
much discussed point in Logic, what is known as 
the inverse variation of Connotation and Denotation. 

Connotation and Denotation are often said to vary 
inversely in quantity. The larger the connotation the 
smaller the denotation, and vice versd. With certain 
qualifications the statement is correct enough, but it 
is a rough compendious way of expressing the facts 
and it needs qualification. 

The main fact to be expressed is that the more 

possessed by all, as risibility. The idea of the Proprium as 
deducible from or consequent on the essence would seem to 
have originated in the desire to find something common to all 
Porphyry's four varieties. 



General Names and Allied Distinctions. 55 

general a name is, the thinner is its meaning. The 
wider the scope, the shallower the ground. As you 
rise in the scale of generality, your classes are wider 
but the number of common attributes is less. Inversely, 
the name of a species has a smaller denotation than 
the name of its genus, but a richer connotation. Fruit- 
tree applies to fewer objects than tree^ but the objects 
denoted have more in common : so with apple and 
fruit-tree^ Ribston Pippin and apple. 

Again, as a rule, if you increase the connotation you 
contract the area within which the name is applicable. 
Take any group of things having certain attributes in 
common, say, men of ability : add courage^ beauty ^ height 
of six feet^ chest measurement of 40 inches^ and with each 
addition fewer individuals are to be found possessing 
all the common attributes. 

This is obvious enough, and yet the expression inverse 
variation is open to objection. For the denotation may 
be increased in a sense without affecting the connotation. 
The birth of an animal may be said to increase the 
denotation : every year thousands of new houses are 
built : there are swarms of flies in a hot summer and 
few in a cold. But all the time the connotation of 
animal^ house, or fly remains the same : the word does 
not change its meaning. 

It is obviously wrong to say that they vary in inverse 
proportion. Double or treble the number of attributes, 
and you do not necessarily reduce the denotation by 
one-half or one-third. 

It is, in short, the meaning or connotation that is 
the main thing. This determines the application of a 
word. As a rule if you increase meaning, you restrict 
scope. Let your idea, notion, or concept of culture 
be a knowledge of Mathematics, Latin and Greek; 



56 Tht Elements of Propositions^ 

your men of culture will be more numerous than if you 
require from each of them these qualifications plus a 
modern language, an acquaintance with the Fine Arts, 
urbanity of manners, etc. 

It is just possible to increase the connotation without 
decreasing the denotation, to thicken or deepen the 
concept without diminishing the class. This is possible 
only when two properties are exactly co-extensive, as 
equilaterality and equiangularity in triangles. 

Singular and Proper Names. A Proper or Singular 
name is a name used to designate an individual. Its 
function, as distinguished from that of the general 
name, is to be used purely for the purpose of distinctive 
reference. 

A man is not called Tom or Dick because he is like 
m certain respects to other Toms or other Dicks. The 
Toms or the Dicks do not form a logical class. The 
names are given purely for purposes of distinction, to 
single out an individual subject. The Arabic equivalent 
for a Proper name, alaniy *' a mark," ** a sign-post," is 
a recognition of this. 

In the expressions "a Napoleon," "a Hotspur," "a 
Harry," the names are not singular names logically, 
but general names logically, used to signify the posses- 
sion of certain attributes. 

A man may be nicknamed on a ground, but if the 
name sticks and is often used, the original meaning is 
forgotten. If it suggests the individual in any one of 
his qualities, any point in which he resembles other 
individuals, it is no longer a Proper or Singular name 
logically, that is, in logical function. That function 
is fulfilled when it has called to mind the individual 
intended. 

To ask, as is sometimes done, whether Proper names 



General Names and Allied Distinctions. 57 

are connotative or denotative, is merely a confusion of 
language. The distinction between connotation and 
denotation, extension and intension, applies only 
to general names. Unless a name is general, it 
has neither extension nor intension : * a Proper or 
Singular name is essentially the opposite of a general 
name and has neither the one nor the other. 

A nice distinction may be drawn between Proper 
and Singular names, though they are strict synonyms 
for the same logical function. It is not essential to 
the discharge of that function that the name should be 
strictly appropriated to one object. There are many 
Toms and many Dicks. It is enough that the word 
indicates the individual without confusion in the 
particular circumstances. 

This function may be discharged by words and 
combinations of words that are not Proper in the 
grammatical sense. " This man," " the cover of this 
book," " the Prime Minister of England," " the seer of 

^ It is a plausible contention that in the case of the Singular 
name the extension is at a minimum and the intension at a 
maximum, the extension being one individual, and the intension 
the totality of his attributes. But this is an inexact and confused 
use of words. A name does not extend beyond the individual 
except when it is used to signify one or more of his prominent 
qualities, that is, is used with the function of a general name. 
The ^jttension of a Singular name is zero : it has no extension. 
On the other hand, it suggests, in its function as a Singular name, 
no properties or qualities ; it suggests only a subject ; i.e,^ it has 
no intension. The ambiguity of the term Denotation helps the 
confusion in the case of Singular names. " Denote " in common 
speech means to indicate, to distinguish. But when in Logic we 
say that a general name denotes individuals, we have no thought 
of indicating or distinguishing : we mean only that it is applicable 
to any one, without respect of individuals, either in predication or 
epithetic description. 



58 The Elements of Propositions. 

Chelsea," may be Singular names as much as Honolulu 
or Lord Tennyson. 

In common speech Singular names are often 
manufactured ad hoc by taking a general name and 
narrowing it down by successive qualifications till it 
applies only to one individual, as "The leading subject 
of the Sovereign of England at the present time ". If 
it so happens that an individual has some attribute or 
combination peculiar to himself, he may be suggested 
by the mention of that attribute or combination : — 
"the inventor of the steam-engine," "the author of 
Hudibras ". 

Have such names a connotation ? The student may 
exercise his wits on the question. It is a nice one, an 
excellent subject of debate. Briefly, if we keep rigid 
hold of the meaning of connotation, this Singular name 
has none. The combination is a singular name only 
when it is the subject of a predication or an attribution, 
as in the sentences, "The position of the leading subject 
of etc., is a difficult one," or " The leading subject oi 
etc., wears an eyeglass". In such a sentence as 
" So-and-so is the leading subject of etc.," the 
combined name has a connotation, but then it is a 
general and not a singular name. 

GollectiYe Names, as distinguished from General 
Names. A collective name is a name for a number ot 
similar units taken as a whole — a name for a totality 
of similar units, as army, regiment, mob, mankind, 
patrimony, personal estate. 

A group or collection designated by a collective name 
is so far like a class that the individual objects have 
something in common : they are not heterogeneous 
but homogeneous. A mob is a collection of human 
beings : a regiment of soldiers ; a library of books. 



General Names and Allied Distinctions. 59 

The distinction lies in this, that whatever is said 
of a collective name is said about the collection as a 
whole, and does not apply to each individual ; what- 
ever is said of a general name applies to each 
individual. Further, the collective name can be 
predicated only of the whole group, as a whole ; the 
general name is predicable of each, distributively. 
** Mankind has been in existence for thousands of 
years;'' "The mob passed through the streets." 
In such expressions as ** An honest man's the noblest 
work of God," the subject is functionally a collective 
name. 

A collective name may be used as a general name 
when it is extended on the ground of what is common 
to all such totalities as it designates. " An excited 
mob is dangerous ; " " An army without discipline is 
useless." The collective name is then " connotative " 
of the common characters of the collection. 

Material or Substantial Names. The question 
has been raised whether names of material, gold, 
water, snow, coal, are general or collective singular 
In the case of pieces or bits of a material, it is true that 
any predicate made concerning the material, such as 
" Sugar is sweet,'' or " Water quenches thirst," applies 
to any and every portion. But the separate portions 
are not individuals in the whole signified by a material 
name as individuals are in a class. Further, the name 
of material cannot be predicated of a portion as a class 
name can be of an individual. We cannot say, " This 
is a sugar ". When we say, " This is a piece of sugar," 
sugar is a collective name for the whole material. 
There are probably words on the borderland between 
general names and collective names. In such expres- 
sions as " This is a coal^'' " The bonnie water o' Urie," 



6o 2%^ Elements of Froposiiians. 

the material name is used as a general name. The 
real distinction is between the distributive use and the 
collective use of a name ; as a matter of grammatical 
usage, the same word may be used either way, but 
logically in any actual proposition it must be either 
one or the other. 

Abstract Names are names for the common attri- 
butes or concepts on which classes are constituted. A 
concrete name is a name directly applicable to an 
individual in all his attributes, that is, as he exists in 
the concrete. It may be written on a ticket and pinned 
to him. When we have occasion to speak of the point 
or points in which a number of individuals resemble 
one another, we use what is called an abstract name, 
" Generous man," " clever man,'' " timid man,'' are 
concrete names; '* generosity," "cleverness," "timidity,'^ 
are abstract names. 

It is disputed whether abstract names are connotative* 
The question is a confused one : it is like asking 
whether the name of a town is municipal. An abstract 
name is the name of a connotation as a separate 
object of thought or reference, conceived or spoken of 
in abstraction from individual accidents. Strictly 
speaking it is notative rather than ^^wnotative : it can- 
not be said to have a connotation because it is itself 
the symbol of what is called the connotation of a 
general name.* 

^ Strictly speaking, as I have tried to indicate all along, the 
words Connotation and Denotation, or Extension and Intension, 
apply only to general names. Outside general names, they have 
no significance. An adjective with its noun is a general name, of 
which the adjective gives part of the Connotation. If we apply 
the word connotation to signify merely the suggestion of an 
attribute in whatever grammatical connexion, then an abstract 



General Names and Allied nistinctions, 6i 

The distinction between abstract names and concrete 
names is virtually a grammatical distinction, that is, 
a distinction in mode of predication. We may use 
concrete names or abstract names at our pleasure to 
express the same meaning. To say that "John 
is a timid man" is the same thing as saying that 
** Timidity is one of the properties or characteristics 
or attributes of John ' . ** Pride and cruelty generally 
go together; " " Proud men are generally cruel men." 

General names are predicable of individuals because 
they possess certain attributes: to predicate the 
possession of those attributes is the same thing as to 
predicate the general name. 

Abstract forms of predication are employed in 
common speech quite as frequently as concrete, and 
are, as we shall see, a great source of ambiguity and 
confusion. 



name is undoubtedly as much connotative as an adjective. The 
word Sweetness has the same meaning as Sweet : it indicates or 
signifies, conveys to the mind of the reader the same attribute : 
the only difference is that it does not at the same time indicate a 
subject in which the attribute is found, sb sweet af>ple. The 
meaning is not f unnoted* 



THE SYLLOGISTIC ANALYSIS OF PROPOSITIONS 
INTO TERMS. 

!• — ^The Bare Analytic Forms, 

The word " term " is loosely used as a mere synonym 
for a name : strictly speaking, a term (opo5, a boundary) 
is one of the parts of a proposition as analysed into 
Subject and Predicate. In Logic, a term is a technical 
word in an analysis made for a special purpose, that 
purpose being to test the mutual consistency of 
propositions. 

For this purpose, the propositions of common 
speech may be viewed as consisting of two Terms, a 
linkword called the copula (positive or negative) 
expressing a relation between them, and certain 
symbols of quantity used to express that relation 
more precisely. 

Let us indicate the Subject term by S, and the 
Predicate term by P. 

All propositions may be analysed into one or other 
of four forms :— 

All S is P, 

No S is P, 
Some S is P, 
Some S is not F* 
(6a) 



The Syllogistic Analysis of Frqposiiions into Terms. 63 

All S is P is called the UniYcrsal AfflrmatiYe, 

and is indicated by the symbol A (the first vowel of 
Affirmo). 

No S is P is called the UniY6Fsal Negative, symbol 
E (the first vowel of Nego). 

Some S is P is called the Particular AflDrmatiTe, 
symbol I (the second vowel of afflxmo). 

Some S is not P is called the Particular Negative, 
symbol O (the second vowel of negO). 

The distinction between Universal and Particular 
is called a distinction in Quantity ; between Affirma- 
tive and Negative, a distinction in Quality, A and E, 
I and O, are of the same quantity, but of different 
quality : A and I, E and O, same in quality, different 
in quantity. 

In this symbolism, no provision is made for expres- 
sing degrees of particular quantity. Some stands for 
any number short of all: it may be one, few, most, 
or all but one. The debates in which Aristotle's 
pupils were interested turned mainly on the proof or 
disproof of general propositions ; if only a proposition 
could be shown to be not universal, it did not matter 
how far or how little short it came. In the Logic of 
Probability, the degree becomes of importance. 

Distinguish, in this Analysis, to avoid subsequent 
confusion, between the Subject and the Subject Term, 
the Predicate and the Predicate Term. The Subject 
is the Subject Term quantified: in A and E,* "AH S"; 

* For perfect symmetry, the form of E should be All S is not P. 
" No S is P " is adopted for E to avoid conflict with a form of 
common speech, in which All S is not P conveys the meaning of 
the Particular Negative. " All advices are not safe " does not 
mean that safeness is denied of all advices, but that safeness 
cannot be affirmed of all, i.*., Not all advices are safe, ».r., some 
are not. 



64 The Elements of Propositions. 

in I and O, " Some S". The Predicate is the Predi- 
cate Term with the Copula, positive or negative : in 
A and I, «* is P " ; in E and O, " is not P '\ 

It is important also, in the interest of exactness, to 
note that S and P, with one exception, represent 
general names. They are symbols for classes. P is 
so always : S also except when the Subject is an 
individual object. In the machinery of the Syllogism, 
predications about a Singular term are treated as 
Universal Affirmatives. ** Socrates is a wise man " 
is of the form All S is P. 

S and P being general names, the signification of 
the symbol " is " is not the same as the ** is " of 
common speech, whether the substantive verb or the 
verb of incomplete predication. In the syllogistic 
form, ** is '* means is contained in^ " is not," is not 
contained in. 

The relations between the terms in the four forms 
are represented by simple diagrams known as Euler's 
circles. 




Diagram 5 is a purely artificial form, having no 
representative in common speech. In the affirmations 
of common speech, P is always a term of greater 
extent than S. 

No. 2 represents the special case where S and P 



The Syllogistic Analysts of Propositions into Terms. 6$ 

are coextensive, as in All equiangular triangles are 
equilateral. 

S and P being general names, they are said to be 
distributed when the proposition applies to them in 
their whole extent, that is, when the assertion covers 
every individual in the class. 

In E, the Universal Negative, both terms are 
distributed : " No S is P " wholly excludes the two 
classes one from the other, imports that not one 
individual of either is in the other. 

In A, S is distributed, but not P. S is wholly in 
P, but nothing is said about the extent of P beyond S. 

In O, S is undistributed, P is distributed. A part of 
S is declared to be wholly excluded from P. 

In I, neither S nor P is distributed. 

It will be seen that the Predicate term of a Negative 
proposition is always distributed, of an Affirmative, 
always undistributed. 

A little indistinctness in the signification of P crept 
into mediaeval text-books, and has tended to confuse 
modern disputation about the import of Predication. 
Unless P is a class name, the ordinary doctrine of 
distribution is nonsense ; and Euler's diagrams are 
meaningless. Yet many writers who adopt both 
follow mediaeval usage in treating P as the equivalent 
of an adjective, and consequently " is '* as identical 
with the verb of incomplete predication in common 
speech. 

It should be recognised that these syllogistic forms 
are purely artificial, invented for a purpose, namely, 
the simplification of syllogising. Aristotle indicated 
the precise usage on which his syllogism is based 

5 



66 The Elements of Propositions. 

{Prior Analytics, i. i and 4). His form * for All S is 
P, is S is wholly in P ; for No S is P, S is wholly not 
in P. His copula is not ** is," but " is in/' and it is 
a pity that this usage was not kept. " All S is in P " 
would have saved much confusion. But^ doubtless 
for the sake of simplicity, the besetting sin of tutorial 
handbooks. All S is P crept in instead, illustrated by 
such examples as **A11 men are mortal". 

Thus the *' is " of the syllogistic form became confused 
with the " is " of common speech, and the syllogistic 
view of predication as being equivalent to inclusion in, 
or exclusion from a class, was misunderstood. The 
true Aristotelian doctrine is not that predication 
consists in referring subjects to classes, but only that 
for certain logical purposes it may be so regarded. 
The syllogistic forms are artificial forms. They 
were not originally intended to represent the actual 
processes of thought expressed in common speech. 
To argue that when I say **A11 crows are black," I 
do not form a class of black things, and contemplate 
crows within it as one circle is within another, is to 
contradict no intelligent logical doctrine. 

The root of the confusion lies in quoting sentences 
from common speech as examples of the logical forms, 
forgetting that those forms are purely artificial. 
*< Omnis homo est mortalis," *' All men are mortal," 
is not an example formally of All S is P. P is a 
symbol for a substantive word or combination of 
words, and mortal is an adjective. Strictly speaking, 
there is no formal equivalent in common speech, that 
is, in the forms of ordinary use — no strict grammatical 

* His most precise form, I should say, for in ** P is predicated 
of every S *' he virtually follows common speech. 



The Syllogistic Analysis of Propositions into Terms, 67 

formal equivalent — for the syllogistic prepositional 
symbols. We can make an equivalent, but it is not 
a form that men would use in ordinary intercourse. 
** All man is in mortal being " would be a strict 
equivalent, but it is not English grammar. 

Instead of disputing confusedly whether All S is P 
should be interpreted in extension or in comprehension, 
it would be better to recognise the original and tradi- 
tional use of the symbols S and P as class names, and 
employ other symbols for the expression in compre- 
hension or connotation. Thus, let s and / stand for 
the connotation. Then the equivalent for All S is 
P would be All S has/, or p always accompanies j, or 
f belongs to all S. 

It may be said that if predication is treated in this 
way, Logic is simplified to the extent of childishness. 
And indeed, the manipulation of the bare forms with 
the help of diagrams and mnemonics is a very humble 
exercise. The real discipline of Syllogistic Logic lies 
in the reduction of common speech to these forms. 

This exercise is valuable because it promotes clear 
ideas about the use of general names in predication, 
their ground in thought and reality, and the liabilities 
to error that lurk in this fundamental instrument of 
speech. 

II. — The Practice of Syllogistic Analysis. 
The basis of the analysis is the use of general names 
in predication. To say that in predication a subject is 
referred to a class, is only another way of saying that 
in every categorical sentence the predicate is a general 
name express or implied : that it is by means of 
general names that we convey our thoughts about 
things to others. 



68 The Elements of Propositions. 

" Milton is a great poet.*' " Quoth Hudibras, 
/ smell a rat,^' Great poet is a general name : it means 
certain qualities, and applies to anybody possessing 
them. Quoth implies a general name, a name for 
persons speakings connoting or meaning a certain act 
and applicable to anybody in the performance of it. 
Quoth expresses also past time : thus it implies another 
general name, a name for persons in past time^ conno- 
ting a quality which differentiates a species in the genus 
persons speaking, and making the predicate term 
** persons speaking in past time ". Thus the proposi- 
tion Quoth Hudibras^ analysed into the syllogistic 
form S is in P, becomes S (Hudibras) is in P (persons 
speaking in past time). The Predicate term P is a 
class constituted on those properties. Smell a rat also 
implies a general name, meaning an act or state 
predicable of many individuals. 

Even if we add the grammatical object of Quoth to 
the analysis, the Predicate term is still a general name. 
Hudibras is only one of the persons speaking in past 
time who have spoken of themselves as being in a 
certain mood of suspicion.^ 

The learner may well ask what is the use of twisting 

1 Remember that when we speak of a general name, we do not 
necessarily mean a single word. A general name, logically 
viewed, is simply the name of a genus^ kind, or class : and 
whether this is single-worded or many-worded is, strictly 
speaking, a grammatical question. " Man," ** man-of-ability," 
" man-of-ability-and-courage," " man-of-ability-and-courage-and- 
gigantic-stature," ** man-who-fought-at-Marathon " — these are 
all general names in their logical function. No matter how the 
constitutive properties of the class are indicated, by one word or 
by a combination, that word or combination is a general name. 
In actual speech we can seldom indicate by a Biagle word the 
meaning predicated. 



The Syllogistic Analysis of Propositions into Terms, 69 

l^ain speech into these uncouth forms. The use is 
certainly not obvious. The analysis may be directly 
useful, as Aristotle claimed for it, when we wish 
to ascertain exactly whether one proposition contra- 
dicts another, or forms with another or others a valid 
link in an argument. This is to admit that it is 
only in perplexing cases that the analysis is of direct 
use. The indirect use is to familiarise us with 
what the forms of common speech imply, and thus 
strengthen the intellect for interpreting the condensed 
and elliptical expression in which common speech 
abounds. 

There are certain technical names applied to the 
components of many-worded general names, Cate- 
gorematic and Syncategorematic, Subject and 
AttributiTe. The distinctions are really grammatical 
rather than logical, and of little practical value. 

A word that can stand by itself as a term is said to 
be Categorematic. Man^ poet^ or any other common 
noun. 

A word that can only form part of a term is 
Syncategorematic. Under this definition come all 
adjectives and adverbs. 

The student's ingenuity may be exercised in applying 
the distinction to the various parts of speech. A verb 
may be said to be Hyper categorematic^ implying, as it 
does, not only a term, but also a copula. 

A nice point is whether the Adjective is cate- 
gorematic or syncategorematic. The question depends 
on the definition of " term " in Logic. In common 
speech an adjective may stand by itself as a predicate, 
and so might be said to be Categorematic. " This 
heart is merry." But if a term is a class, or the name 
of a class, it is not Categorematic in the above 



7© TAe Elements of Propositions. 

definition. It can only help to specify a class when 
attached to the name of a higher genus. 

Mr. Fowler's words Subject and Attributive 
express practically the same distinction, except that 
Attributive is of narrower extent than syncategorematic. 
An Attributive is a word that connotes an attribute or 
property, as hot^ valorous^ and is always grammatically 
an adjective. 

The expression of Quantity, that is, of Universality 
or non-universality, is all-important in syllogistic 
formulae. In them universality is expressed by Ail 
or None. In ordinary speech universality is expressed 
in various forms, concrete and abstract, plain and 
figurative, without the use of ** all *' or " none ". 

Uneasy lies the head that wears a crown. 
He can't be wrong whose life is, in the right. 
What cat's averse to fish ? 
Can the leopard change his spots ? 
The longest road has an end. 
Suspicion ever haunts the guilty mind. 
Irresolution is always a sign of weakness* 
Treason never prospers. 

A proposition in which the quantity is not expressed 
is called by Aristotle Indefinite (dStd/oto-Tos). For 
"indefinite"* Hamilton suggests Preindesignate, 

1 The objection taken to the word "indefinite," that the 
quantity of particular propositions is indefinite, some meaning 
any quantity less than all, is an example of the misplaced and 
frivolous subtlety that has done so much to disorder the tradition 
of Logic. By " indefinite " is simply meant not definitely 
expressed as either Universal or Particular, Total or Partial. 
The same objection might be taken to any word used to express 
the distinction : the degree of quantity in Some S is not 
** designate " any more than it is " definite " or " dioristic ". 



The Syllogistic Analysis of Propositions into Terms, 71 

undesignated, that is, before being received from common 
speech for the syllogistic mill. A proposition is 
Predesignate when the quantity is definitely indicated. 
All the above propositions are " Predesignate " uni- 
versals, and reducible to the form All S is P, or No 
S is P. 

The following propositions are no less definitely 
particular, reducible to the form I or 0. In them as 
in the preceding quantity is formally expressed, though 
the forms used are not the artificial syllogistic forms :— 

Afflictions are often salutary. 
Not every advice is a safe one. 
All that glitters is not gold. 
Rivers generally * run into the sea. 

Often, however, it is really uncertain from the form 
of common speech whether it is intended to express a 
universal or a particular. The quantity is not formally 
expressed. This is especially the case with proverbs 
and loose floating sayings of a general tendency. For 
example : — 

Haste makes waste. 

Knowledge is power. 

Light come, light go. 

Left-handed men are awkward antagonists. 

Veteran soldiers are the steadiest in fight. 

^ Generally, In this word we have an instance of the frequent con- 
flict between the words of common speech and logical terminology. 
How it arises shall be explained in next chapter. A General pro- 
position is a synonym for a Universal proposition (if the forms A 
and E are so termed) : but " generally " in common speech means 
** for the most part,'* and is represented by the symbol of par- 
ticular quantity, Some 



J 2 The Elements of Propositions. 

Such sayings are in actual speech for the most part 
delivered as universals.^ It is a useful exercise of the 
Socratic kind to decide whether they are really so, 
This can only be determined by a survey of facts. The 
best method of conducting such a survey is probably 
(i) to pick out the concrete subject, '* hasty actions," 
"men possessed of knowledge," ** things lightly 
acquired " ; (2) to fix the attribute or attributes predi- 
cated; (3) to run over the individuals of the subject 
class and settle whether the attribute is as a matter oi 
fact meant to be predicated of each and every one. 

This is the operation of Induction. If one individual 
can be found of whom the attribute is not meant to be 
predicated, the proposition is not intended as Uni- 
versal. 

Mark the difference between settling what is intended 
and settling what is true. The conditions of truth and 
the errors incident to the attempt to determine it, are 
the business of the Logic of Rational Belief, commonly 
entitled Inductive Logic. The kind of "induction" 
here contemplated has for its aim merely to determine 
the quantity of a proposition in common acceptation, 
which can be done by considering in what cases the 
proposition would generally be alleged. This corre- 
sponds nearly as we shall see to Aristotelian Induction, 
the acceptance of a universal statement when no 
instance to the contrary is alleged. 

It is to be observed that for this operation we do not 

1 With some logicians it is a mechanical rule in reducing to 
syllogistic form to treat as I or O all sentences in which there is 
no formal expression of quantity. This is to err on the safe side, 
but common speakers are not so guarded, and it is to be presumed 
rather that they have a universal application in their minds when 
they do not expressly qualify, 



The Syllogistic Analysis of Propositions into Terms, 73 

practically use the syllogistic form All S is P. We do 
not raise the question Is All S, P ? That is, we do not 
constitute in thought a class P : the class in our minds 
is S, and what we ask is whether an attribute predicated 
of this class is truly predicated of every individual 
of it. 

Suppose we indicate by / the attribute, knot of 
attributes, or concept on which the class P is consti- 
tuted, then All S is P is equivalent to " All S has/ '' : 
and Has All S/ ? is the form of a question that we 
have in our minds when we make an inductive survey 
on the above method. I point this out to emphasise 
the fact that there is no prerogative in the form All S 
is P except for syllogistic purposes. 

This inductive survey may be made a useful 
Collateral Discipline. The bare forms of Syllogistic 
are a useless item of knowledge unless they are 
applied to concrete thought. And determining the 
quantity of a common aphorism or saw, the limits 
within which it is meant to hold good, is a valuable 
discipline in exactness of understanding. In trying 
to penetrate to the inner intention of a loose general 
maxim, we discover that what it is really intended 
to assert is a general connexion of attributes, and a 
survey of concrete cases leads to a more exact ap- 
prehension of those attributes. Thus in considering 
whether Knowledge is power is meant to be asserted 
of all knowledge, we encounter along with such 
examples as the sailor's knowledge that wetting a 
rope shortens it, which enabled some masons to raise 
a stone to its desired position, or the knowledge of 
French roads possessed by the German invaders, — 
along with such examples as these we encounter cases 
where a knowledge of difficulties without a knowledge 



74 The Elements of Propositions. 

of the means of overcoming them is paralysing to 
action. Samuel Daniel says : — 

Where timid knowledge stands considering 
Audacious ignorance has done the deed. 

Studying numerous cases where ** Knowledge is 
power" is alleged or denied, we find that what is 
meant is that a knowledge of the right means of 
doing anything is power — in short, that the predicate 
is not made of all knowledge, but only of a species 
of knowledge. 

Take, again, Custom blunts sensibility. Putting this 
in the concrete, and inquiring what predicate is made 
about **men accustomed to anything" (S), we have 
no difficulty in finding examples where such men are 
said to become indifferent to it. We find such illus- 
trations as Lovelace's famous " Paradox " ;— 

Through foul we follow fair 

For had the world one face 
And earth heen bright as air 

We had known neither place. 
Indians smell not their nest 
The Swiss and Finn taste best 

The spices of the East. 

So men accustomed to riches are not acutely sensible 
of their advantages : dwellers in noisy streets cease to 
be distracted by the din : the watchmaker ceases to 
hear the multitudinous ticking in his shop : the 
neighbours of chemical works are not annoyed by the 
smells like the casual passenger. But we find also 
that wine-tasters acquire by practice an unusual 
delicacy of sense ; that the eyes once accustomed to 
a dim light begin to distinguish objects that were at 



The Syllogistic Analysis of Propositions into Terms, 75 

first indistinguishable; and so on. What meanings 
of ** custom " and of " sensibility " will reconcile these 
apparently conflicting examples ? What are the exact 
attributes signified by the names ? We should probably 
find that by sensibility is meant emotional sensibility 
as distinguished from intellectual discrimination, and 
that by custom is meant familiarity with impressions 
whose variations are not attended to, or subjection to 
one unvarying impression. 

To verify the meaning of abstract proverbs in this 
way is to travel over the road by which the Greek 
dialecticians were led to feel the importance of 
definition. Of this more will be said presently. If 
it is contended that such excursions are beyond the 
bounds of Formal Logic, the answer is that the 
exercise is a useful one and that it starts naturally 
and conveniently from the formulae of Logic. It is the 
practice and discipline that historically preceded the 
Aristotelian Logic, and in the absence of which the 
Aristotelian formulae would have a narrowing and 
cramping effect. 

Can all propositions be reduced to the syllogistic 
form ? Probably: but this is a purely scientific inquiry, 
collateral to Practical Logic. The concern of Practical 
Logic is chiefly with forms of proposition that favour 
inaccuracy or inexactness of thought. When there is 
no room for ambiguity or other error, there is no virtue 
in artificial syllogistic form. The attempt so to reduce 
any and every proposition may lead, however, to the 
study of what Mr. Bosanquet happily calls the 
" Morphology " of Judgment, Judgment being the 
technical name for the mental act that accompanies 
the utterance of a proposition. Even in such sentences 
as " How hot it is ! " or " It rains," the rudiment of 



76 The Elements of Propositions. 

subject and predicate may be detected. When a man 
says "How hot it is," he conveys the meaning, though 
there is no definitely formed subject in his mind, that 
the outer world at the moment of his speaking has a 
certain quality or attribute. So with " It rains ". The 
study of such examples in their context, however, reveals 
the fact that the same form of Common speech may 
cover different subjects and predicates in different 
connexions. Thus in the argument:— 

" Whatever is, is best. 
It rains : "— 

the Subject is Rain and the Predicate is now^ " is at 
the present time," " is in the class of present events". 

III. — Some Technical Difficulties. 

The formula for Exclusive Propositions. " None 
but the brave deserve the fair" : ** No admittance 
except on business'' : ** Only Protestants can sit on the 
throne of England ". 

These propositions exemplify different ways in 
common speech of naming a subject exclusively^ the 
predication being made of all outside a certain term. 
" None that are not brave, etc. ; " ** none that are not 
on business, etc.;" '* none that are not Protestants, 
etc". No not-S is P. It is only about all outside the 
given term that the universal assertion is made : we 
say nothing universally about the individuals within 
the term : we do not say that all Protestants are 
eligible, nor that all persons on business are admitted, 
nor that every one of the brave deserves the fair. All 
that we say is that the possession of the attribute 
named is an indispensable condition: a person may 



I'Ae Syllogistic Analysis of Propositions into Terms, 77 

possess the attribute, and yet on other grounds may 
not be entitled to the predicate. 

The justification for taking special note of this form 
in Logic is that we are apt by inadvertence to make an 
inclusive inference from it. Let it be said that None 
but those who work hard can reasonably expect to 
pass, and we are apt to take this as meaning that all 
who work hard may reasonably expect to pass. But 
what is denied of every Not-S is not necessarily 
affirmed of every S. 

The expression of Tense or Time in the Syllogistic 
Forms, Seeing that the Copula in S is P or S is in P 
does not express time, but only a certain relation 
between S and P, the question arises Where are we to 
put time in the analytic formula ? ** Wheat is dear ; " 
" All had fled ;" time is expressed in these propositions, 
and our formula should render the whole content of 
what is given. Are we to include it in the Predicate 
term or in the Subject term ? If it must not be left 
out altogether, and we cannot put it with the copula, 
we have a choice between the two terms. 

It is a purely scholastic question. The common 
technical treatment is to view the tense as part of the 
predicate. " All had fled," All S is P, i.e., the whole 
subject is included in a class constituted on the 
attributes of flight at a given time. It may be that the 
Predicate is solely a predicate of time. ** The Board 
met yesterday at noon." S is P, />., the meeting of 
the Board is one of the events characterised by having 
happened at a certain time, agreeing with other events 
in that respect. 

But in some cases the time is more properly regarded 
as part of the subject. E,g,, ** Wheat is dear'*. S 
does BOt here stand for wheat collectively, but for the 



78 The Elements of Propositiom. 

wheat now in the market, the wheat of the present 
time : it is concerning this that the attribute of dearness 
is predicated ; it is this that is in the class of dear 
things. 

The expression of Modality in the Syllogistic Forms, 
Propositions in which the predicate is qualified by an 
expression of necessity, contingency, possibility or 
impossibility [/.e., in English by must^ may^ can^ or 
cannot]^ , were called in Mediaeval Logic Modal Proposi- 
tions. " Two and two must make four." " Grubs 
may become butterflies." ** Z can paint." " Y cannot 

fly." 

There are two recognised ways of reducing such 
propositions to the form S is P. One is to distinguish 
between the Dictum and the Mode, the proposition and 
the qualification of its certainty, and to treat the Dictum 
as the Subject and the Mode as the Predicate. Thus : 
" That two and two make four is necessary " ; " That 
Y can fly is impossible ". 

The other way is to treat the Mode as part of the 
predicate. The propriety of this is not obvious in the 
case of Necessary propositions, but it is unobjectionable 
in the case of the other three modes. Thus : " Grubs 
are things that have the potentiality of becoming 
butterflies " ; " Z has the faculty of painting " ; " Y 
has not the faculty of flying ". 

The chief risk of error is in determining the quantity 
of the subject about which the Contingent or Possible 
predicate is made. When it is said that ** Victories 
may be gained by accident,'' is the predicate made 
concerning All victories or Some only ? Here we are 
apt to confuse the meaning of the contingent assertion 
with the matter of fact on which in common belief it 
rests. It is true only that some victories have been 



The Syllogistic Analysis of Propositions into Terms, 79 

gained by accident, and it is on this ground that we 
assert in the absence of certain knowledge concerning 
any victory that it may have been so gained. The 
latter is the effect of the contingent assertion : it is 
made about any victory in the absence of certain 
knowledge, that is to say, formally about all. 

The history of Modals in Logic is a good illustration 
of intricate confusion arising from disregard of a 
clear traditional definition. The treatment of them by 
Aristotle was simple, and had direct reference to tricks 
of disputation practised in his time. He specified four 
" modes," the four that descended to mediaeval logic, 
and he concerned himself chiefly with the import 
of contradicting these modals. What is the true 
contradictory of such propositions as, ** It is possible 
to be" (Swaror ctmt), ** It admits of being" (evScxcrat 
cTvai), " It must be " (dmyKaioi/ ctvat), " It is impossible 
to be " (aSwarov ctrat) ? What is implied in saying 
** No " to such propositions put interrogatively ? " Is 
it possible for Socrates to fly ? " " No." Does this 
mean that it is not possible for Socrates to fly, or that 
it is possible for Socrates not to fly ? 

A disputant who had trapped a respondent into 
admitting that it is possible for Socrates not to fly, 
might have pushed the concession farther in some 
such way as this : *« Is it possible for Socrates not 
to walk ? " " Certainly.'' " Is it possible for him to 
walk ? " " Yes." " When you say that it is possible 
for a man to do anything do you not believe that it is 
possible for him to do it ? " *' Yes." ** But you have 
admitted that it is possible for Socrates not to fly ? " 

It was in view of such perplexities as these that 
Aristotle set forth the true contradictories of his four 
Modals. We may laugh at such quibbles now and 



8o The Elements of Propositions. 

wonder that a grave logician should have thought 
them worth guarding against. But historically this 
is the origin of the Modals of Formal Logic, and to 
divert the names of them to signify other distinctions 
than those between modes of qualifying the certainty 
of a statement is to introduce confusion. 

Thus we find "Alexander was a great general," given 
as an example of a Contingent Modal, on the ground 
that though as a matter of fact Alexander was so he 
might have been otherwise. It was not necessary that 
Alexander should be a great general : therefore the 
proposition is contingent. Now the distinction between 
Necessary truth and Contingent truth may be important 
philosophically : but it is merely confusing to call the 
character of propositions as one or the other by the 
name of Modality. The original Modality is a mode 
of expression : to apply the name to this character is 
to shift its meaning. 

A more simple and obviously unwarrantable depar- 
ture from tradition is to extend the name Modality to 
any grammatical qualification of a single verb in 
common speech. On this understanding '* Alexander 
conquered Darius '' is given by Hamilton as a Pure 
proposition, and "Alexander conquered Darius honour- 
ably '* as a Modal, This is a merely grammatical 
distinction, a distinction in the mode of composing the 
predicate term in common speech. In logical tradition 
Modality is a mode of qualifying the certainty of an 
affirmation. " The conquest of Darius by Alexander 
was honourable," or " Alexander in conquering Darius 
was an honourable conqueror," is the syllogistic form 
of the proposition : it is simply assertory, not qualified 
in any " mode". 

There is a similar misunderstanding in Mr. Shedden's 



The Syllogistic Analysis of Propositions into Terms. 8i 

treatment of " generally " as constituting a Modal in 
such sentences, as ** ^vwtx^ generally flow into the sea *'. 
He argues that as generally is not part either of the 
Subject term or of the Predicate term, it must belong 
to the Copula, and is therefore a modal qualification of 
the whole assertion. He overlooked the fact that the 
word " generally " in an expression of Quantity : it 
determines the quantity of the Subject term. 

Finally it is sometimes held (^.^., by Mr. Venn) that 
the question of Modality belongs properly to Scientific 
or Inductive Logic, and is out of place in Formal 
Logic. This is so far accurate that it is for Inductive 
Logic to expound the conditions of various degrees of 
certainty. The consideration of Modality is pertinent 
to Formal Logic only in so far as concerns special 
perplexities in the expression of it. The treatment of 
it by Logicians has been rendered intricate by torturing 
the old tradition to suit different conceptions of the end 
and aim of Logic- 



PART II. 
DEFINITION. 

Chapter I. 

IMPERFECT UNDERSTANDING OF WORDS AND THE 
REMEDIES THEREFOR. — DIALECTIC. — DEFINI- 
TION. 

We cannot inquire far into the meaning of proverbs or 
traditional sayings without discovering that the com- 
mon understanding of general and abstract names is 
loose and uncertain. Common speech is a quicksand. 
Consider how we acquire our vocabulary, how we 
pick up the words that we use from our neighbours and 
from books, and why this is so soon becomes apparent. 
Theoretically we know the full meaning of a name 
^when we know all the attributes that it connotes, and 
we are not justified in extending it except to objects 
that possess all the attributes. This is the logical ideal, 
but between the ought to be of Logic and the is of 
practical life, there is a vast difference. How seldom 
do we conceive words in their full meaning ! And who 
is to instruct us in the full meaning ? It is not as in 
the exact sciences, where we start with a knowledge of 

(82) 



Imperfect Undersiandmg of Words, 83 

the full meaning. In Geometry, for example, we learn 
the definitions of the words used, pointy line^ parallel^ 
etc., before we proceed to use them. But in common 
speech, we learn words first in their application to I 
individual cases. Nobody ever defined good to us, or 
fair^ ox kind^ or highly educated. We hear the words 
applied to individual objects: we utter them in the 
same connexion : we extend them to other objects that 
strike us as like without knowing the precise points 
of likeness that the convention of common speech 
includes. The more exact meaning we learn by/ 
gradual induction from individual cases. Ugly^ beauti-^ 
ful^ good^ bad — we learn the words first as applicable to 
things and persons : gradually there arises a more or 
less definite sense of what the objects so designated 
have in common. The individual's extension of the 
name proceeds upon what in the objects has most 
impressed him when he caught the word : this may 
differ in different individuals ; the usage of neighbours 
corrects individual eccentricities. The child in arms 
shouts Da at the passing stranger who reminds him 
of his father: for him at first it is a general name 
applicable to every man : by degrees he learns that 
for him it is a singular name. 

The mode in which words are learnt and extended 
may be studied most simply in the nursery. A child, 
say, has learnt to say mambro when it sees its nurse. 
The nurse works a hand-turned sewing machine, and 
sings to it as she works. In the street the child sees 
an organ-grinder singing as he turns his handle : it 
calls mambro : the nurse catches the meaning and the 
child is overjoyed. The organ-grinder has a monkey: 
the child has an india-rubber monkey toy : it calls this 
also mambro. The name is extended to a monkey in 



84 Definition. 

a picture-book. It has a toy musical box with a 
handle : this also becomes mambro^ the word being 
extended along another line of resemblance. A stroller 
with a French fiddle comes within the denotation of 
the word : a towel-rail is also called mambro from some 
fancied resemblance to the fiddle. A very swarthy 
hunch-back mambro frightens the child : this leads to 
the transference of the word to a terrific coalman with 
a bag of coals on his back. In a short time the word 
has become a name for a great variety of objects that 
have nothing whatever common to all of them, though 
each is strikingly like in some point to a predecessor 
in the series. When the application becomes too 
heterogeneous, the word ceases to be of use as a 
sign and is gradually abandoned, the most impressive 
meaning being the last to go. In a child^s vocabulary 
where the word mambro had a run of nearly two years, 
its last use was as an adjective signifying ugly or 
horrible. 

The history of such a word in a child's language is 
a type of what goes on in the language of men. In 
the larger history we see similar extensions under 
similar motives, checked and controlled in the same 
way by surrounding usage. 

It is obvious that to avoid error and confusion, the 
meaning or connotation of names, the concepts, should 
somehow be fixed : names cannot otherwise have an 
identical reference in human intercourse. We may 
call this ideal fixed concept the Logical Concept : or 
we may call it the Scientiflc Concept, inasmuch as 
one of the main objects of the sciences is to attain 
such ideals in different departments of study. But in 
actual speech we have also the Personal Concept, 
which varies more or less with the individual user, 



Imperfect Understanding of Words. 85 

and the Popular or Yernacular Concept, which, 
though roughly fixed, varies from social sect to social 
sect and from generation to generation. 

The variations in Popular Concepts may be traced 
in linguistic history. Words change with things and 
with the aspects of things, as these change in public 
interest and importance. As long as the attributes 
that govern the application of words are simple, 
sensible attributes, little confusion need arise : the 
variations are matters of curious research for the 
philologist, but are logically insignificant. Murray's 
Dictionary, or such books as Trench's English Past 
and Present^ supply endless examples, as many, indeed 
as there are words in the language. Clerk has almost 
as many connotations as our typical mambro: clerk 
in holy orders, church clerk, town clerk, clerk of 
jLSsize, grocer's clerk. In Early English, the word 
meant " man in a religious order, cleric, clergyman " ; 
ability to read, write, and keep accounts being a 
prominent attribute of the class, the word was 
extended on this simple ground till it has ceased 
altogether to cover its original field except as a 
formal designation. But no confusion is caused by 
the variation, because the property connoted is 
simple.* So with any common noun : street, carriage, 
ship, house, merchant, lawyer, professor. We might 
be puzzled to give an exact definition of such words, 



^ Except, perhaps, in new offices to which the name is extended, 
such as Clerk of School Board. The name, bearing its most 
simple and common meaning, may cause popular misapprehension 
of the nature of the duties. Any uncertainty in meaning may be 
dangerous in practice : elections have been affected by the 
ambiguity of this word. 



86 Definition, 

to say precisely what they connote in common usage ; 
but the risk of error in the use of them is small. 

When we come to words of which the logical con- 
cept is a complex relation, an obscure or intangible 
attribute, the defects of the popular conception and its 
tendencies to change and confusion, are of the greatest 
practical importance. Take such words as Monarchy^ 
tyranny^ civil freedom^ freedom of contract^ landlord^ 
gentleman^ prig^ culture, education, temperance, generosity. 
Not merely should we find it difficult to give an 
analytic definition of such words : we might be unable 
to do so, and yet flatter ourselves that we had a clear 
understanding of their meaning. But let two men 
begin to discuss any proposition in which any such 
word is involved, and it will often be found that they 
take the word in different senses. If the relation 
expressed is complex, they have different sides or lines 
of it in their minds; if the meaning is an obscure 
quality, they are guided in their application of it \rj 
different outward signs. 

Monarchy, in its original meaning, is applied to a 
form of government in which the will of one man is 
supreme, to make laws or break them, to appoint or 
dismiss officers of state and justice, to determine peace 
or war, without control of statute or custom. But 
supreme power is never thus uncontrolled in reality ; 
and the word has been extended to cover governments 
in which the power of the titular head is controlled in 
many diflferent modes and degrees. The existence of 
a head, with the title of King or Emperor, is the 
simplest and most salient fact : and wherever this 
exists, the popular concept of a monarchy is realised. 
The President of the United States has more real 
power than the Sovereign of Great Britain ; but the 



Imperfect Vtiderstanding of Words, 87 

one government is called a Republic and the other 
a Monarchy. People discuss the advantages and 
disadvantages of monarchy without first deciding 
whether they take the word in its etymological sense 
of unlimited power, or its popular sense of titular 
kingship, or its logical sense of power definitely 
limited in certain ways. And often in debate, 
monarchy is really a singular term for the government 
of Great Britain. 

Culture, religious, generous, are names for inward 
states or qualities : with most individuals some simple 
outward sign directs the application of the word — it 
may be manner, or bearing, or routine observances, or 
even nothing more significant than the cut of the 
clothes or of the hair. Small things undoubtedly are 
significant, and we must judge by small things when 
we have nothing else to go by : but instead of trying 
to get definite conceptions for our moral epithets, and 
suspending judgment till we know that the use of the 
epithet is justified, the trifling superficial sign becomes 
for us practically the whole meaning of the word. We 
feel that we must have a judgment of some sort at 
once : only simple signs are suited to our impatience. 

It was with reference to this state of things that 
Hegel formulated his paradox that the true abstract 
thinker is the plain man who laughs at philosophy as 
what he calls abstract and unpractical. He holds 
decided opinions for or against this or the other 
?ih^\.T^QX\on, freedom, tyranny, revolution, reform, socialism, 
but what these words mean and within what limits the 
things signified are desirable or undesirable, he is in 
too great a hurry to pause and consider. 

The disadvantages of this kind of " abstract" think- 
ing are obvious. The accumulated wisdom of man- 



88 Definition. 

kind is stored in language. Until we have cleared our 
conceptions, and penetrated to the full meaning of 
words, that wisdom is a sealed book to us. Wise 
maxims are interpreted by us hastily in accordance 
with our own narrow conceptions. All the vocables of a 
language may be more or less familiar to us, and yet 
we may not have learnt it as an instrument of thought. 
Outside the very limited range of names for what we 
see and use in the daily routine of life, food and clothes 
and the common occupations of men, words have little 
meaning for us, and are the vehicles merely of thin 
preconceptions and raw prejudices. 

The remedy for '^abstract " thinking is more thinking, 
and in pursuing this two aims may be specified for the 
pake of clearness, though they are closely allied, and 
progress towards both may often be made by one and 
the same operation, (i) We want to reach a clear and 
full conception of the meaning of names as used now 
or at a given time. Let us call this the Verification of 
the Meaning. (2) We want to fix such conceptions, 
and if necessary readjust their boundaries. This is the 
province of Definition^ which cannot be effectually per- 
formed without Scientific Classification or Division. 

I. — ^Verification of the Meaning — Dialectic. 

This can only be done by assembling the objects 
to which the words are applied, and considering what 
they have in common. To ascertain the actual 
connotation we must run over the actual denotation. 
And since in such an operation two or more minds are 
better than one, discussion or dialectic is both more 
fruitful and more stimulating than solitary reflection 
or reading. 



Verification of Meaning. 89 

The first to practise this process on a memorable 
scale, and with a distinct method and purpose, was 
Socrates. To insist upon the necessity of clear 
conceptions, and to assist by his dialectic procedure 
in forming them, was his contribution to philosophy. 

His plan was to take a common name, profess 
ignorance of its meaning, and ask his interlocutor 
whether he would apply it in such and such an 
instance, producing one after another. According to 
Xenophon's Memorabilia he habitually chose the 
commonest names, good^ unjust^ fittings and so forth, 
and tried to set men thinking about them, and 
helped them by his questions to form an intelligent 
conception of the meaning. 

For example, what is the meaning of injustice ? 
Would you say that the man who cheats or deceives 
is unjust ? Suppose a man deceives his enemies, is 
there any injustice in that ? Can the definition be 
that a man who deceives his friends is unjust ? But 
there are cases where friends are deceived for their 
own good : are these cases of injustice ? A general 
may inspirit his soldiers by a falsehood. A man 
may cajole a weapon out of his friend's hand when 
he sees him about to commit suicide. A father may 
deceive his son into taking medicine. Would you 
call these men unjust ? By some such process of 
interrogation we are brought to the definition that 
a man is unjust who deceives his friends to their 
hurt. 

Observe that in much of his dialectic the aim of 
Socrates was merely to bring out the meaning lying 
vague and latent, as it were, in the common mind. 
His object was simply what we have called the 
verification of the meaning. And a dialectic that 



90 Definition. 

confines itself to the consideration of what is ordir 
arily meant as distinct from what ought to be meant 
may often serve a useful purpose. Disputes about 
words are not always as idle as is sometimes 
supposed. Mr. H. Sidgwick truly remarks (a propos 
of the terms of Political Economy) that there is 
often more profit in seeking a definition than in 
finding it. Conceptions are not merely cleared but 
deepened by the process. Mr. Sidgwick's remarks 
are so happy that I must take leave to quote them : 
they apply not merely to the verification of ordinary 
meaning but also to the study of special uses by 
authorities, and the reasons for those special uses. 

" The truth is — as most readers of Plato know, only it is 
a truth difficult to retain and apply — that what we gain by 
discussing a definition is often but slightly represented in 
the superior fitness of the formula that we ultimately adopt; 
it consists chiefly in the greater clearness and fulness in 
which the characteristics of the matter to which the 
formula refers have been brought before the mind in the 
process of seeking for it. While we are apparently aiming 
at definitions of terms, our attention should be really fixed 
on distinctions and relations of fact. These latter are what 
we are concerned to know, contemplate, and as far as 
possible arrange and systematise ; and in subjects where 
we cannot present them to the mind in ordinary fulness by 
the exercise of the organs of sense, there is no way of 
surveying them so convenient as that of reflecting on our 
use of common terms. ... In comparing different definitions 
our aim should be far less to decide which we ought to 
adopt, than to apprehend and duly consider the grounds on 
which each has commended itself to reflective minds. We 
shall generally find that each writer has noted some 
relation, some resemblance or difference, which others have 
overlooked ; and we shall gain in completeness, and often 



Verification of Meaning, 91 

in precision^ of view by following him in his observations, 
whether or not we follow him in his conclusions." * 

Mr. Sidgwick's own discussions of Wealthy Value^ 
and Money are models. A clue is often found to the 
meaning in examining startlingly discrepant state^ 
ments connected with the same leading word. Thus 
we find some authorities declaring that " style '' cannot 
be taught or learnt, while others declare that it can. 
But on trying to ascertain what they mean by " style," 
we find that those who say it cannot be taught mean 
either a certain marked individual character or manner 
of writing — as in Buffon's saying, Le style c'est Vhommt 
meme — or a certain felicity and dignity of expression^ 
while those who say style can be taught mean lucid 
method in the structure of sentences or in the arrange- 
ment of a discourse. Again in discussions on the 
rank of poets, we find different conceptions of what 
constitutes greatness in poetry lying at the root of 
the inclusion of this or the other poet among great 
poets. We find one poet excluded from the first rank 
of greatness because his poetry was not serious ; 
another because his poetry was not widely popular ; 
another because he wrote comparatively little; another 
because he wrote only songs or odes and never 
attempted drama or epic. These various opinions 
point to different conceptions of what constitutes 
greatness in poets, different connotations of " great 
poet". Comparing different opinions concerning 
" education " we may be led to ask whether it means 
more than instruction in the details of certain subjects, 
whether it does not also import the formation of a 

1 Sidgwick's Political Economy, pp. 52-3: Ed. 1883, 



99 Definition. 

disposition to learn or an interest in learning or 
instruction in a certain method of learning. 

Historically, dialectic turning on the use of words 
preceded the attempt to formulate principles of Defini- 
tion, and attempts at precise definition led to Division 
and Classification, that is to systematic arrangement 
of the objects to be defined. Attempt to define any 
such word as " education,'* and you gradually become 
sensible of the needs in respect of method that forced 
themselves upon mankind in the history of thought. 
You soon become aware that you cannot define it by 
itself alone ; that you are beset by a swarm of more or 
less synonymous words, instruction^ discipUne^ culture^ 
trainings and so on ; that these various words represent 
distinctions and relations among things more or less 
Rllied ; and that, if each must be fixed to a definite 
meaning, this must be done with reference to one 
another and to the whole department of things that 
they cover. 

The first memorable attempts at scientific arrange- 
ment were Aristotle's treatises on Ethics and Politics, 
which had been the subjects of active dialectic 
for at least a century before. That these the most 
difficult of all departments to subject to scientific 
treatment should have been the first chosen was due 
simply to their preponderating interest : " The proper 
study of mankind is man ". The systems of what are 
known as the Natural Sciences are of modern origin : 
the first, that of Botany, dates from Cesalpinus in 
the sixteenth century. But the principles on which 
Aristotle proceeded in dividing and defining, principles 
which have gradually themselves been more precisely 
formulated, are principles applicable to all systematic 



Fixation of Meaning. 93 

arrangements for purposes of orderly study. I give 
them in the precise formulae which they have gradually 
assumed in the tradition of Logic. The principles of 
Division are often given in Formal Logic, and the 
principles of Classification in Inductive Logic, but 
there is no valid reason for the separation. The 
classification of objects in the Natural Sciences, of 
animals, plants, and stones, with a view to the thorough 
study of them in form, structure, and function, is more 
complex than classifications for more limited purposes, 
and the tendency is to restrict the word classification to 
these elaborate systems. But really they are only a 
series of divisions and subdivisions, and the same 
principles apply to each of the subordinate divisions 
as well as to the division of the whole department 
of study. 

IL — Principles of Division or Classification and 
Definition. 

Confusion in the boundaries of names arises from 
confused ideas regarding the resemblances and 
differences of things. As a protective against this 
confusion, things must be clearly distinguished in 
their points of likeness and difference, and this 
leads to their arrangement in systems, that is, to 
division and classification. A name is not secure 
against variation until it has a distinct place in 
such a system as a symbol for clearly distinguished 
attributes. Nor must we forget, further, that systems 
have their day, that the best system attainable is 
only temporary, and may have to be recast to 
correspond with changes of things and oif man's 
way of looking at them. 



94 Definition. 

The leading principles of Division may be stated 
as follows: — 

I. Every division is made on the ground of differences 
I in some attribute common to all the members of 

the whole to be divided. 

This is merely a way of stating what a logical 
division is. It is a division of a generic whole or 
genusy an indefinite number of objects thought of 
together as possessing some common character or 
attribute. All have this attribute, which is technically 
called the fundamentum divisionis^ or generic attribute. 
But the whole is divisible into smaller groups {species\ 
each of which possesses the common character with 
a difference {differentia). Thus, mankind may be 
divided into White men. Black men. Yellow men, on 
ground of the differences in the colour of their skins : 
all have skins of some colour: this is ^^fundamentum 
divisionis: but each subdivision or species has a 
different colour: this is the differentia. Rectilineal 
figures are divided into triangles, quadrangles, 
pentagons, etc., on the ground of differences in the 
number of angles. 

Unless there is 2, fund, div.^ />., unless the differences 
are differences in a common character, the division is 
not a logical division. To divide men into Europeans, 
opticians, tailors, blondes, brunettes, and dyspeptics 
is not to make a logical division. This is seen more 
clearly in connexion with the second condition of ^ 
perfect division. 

1 II. In a perfect division, the subdivisions or species 
1 are mutually exclusive. 

Every object possessing the common character 



Fixation of Meaning. 95 

should be in one or other of the groups, and none 
should be in more than one. 

Confusion between classes, or overlapping, may 
arise from two causes. It may be due (i) to faulty 
division, to want of unity in Xh^ fundamentum divisiofiis; 
(2) to the indistinct character of the objects to be 
defined. 

(i) Unless the division is based upon a single ground, \ 
unless each species is based upon some mode of the | 
generic character, confusion is almost certain to arise.- 
Suppose the field to be divided, the objects to be 
classified, are three-sided rectilineal plane figures, 
each group must be based upon some modification of 
the three sides. Divide them into equilateral, isosceles, 
and scalene according as the three sides are all of 
equal length, or two of equal length, or each of 
different length, and you have a perfect division. 
Similarly you can divide them perfectly according to 
the character of the angles into acute-angled, right- 
angled and obtuse-angled. But if you do not keep 
to a single basis, as in dividing them into equilateral. 
Isosceles, scalene, and right-angled, you have a cross- 
division. The same triangle might be both right- 
angled and isosceles. 

(2) Overlapping, however, may be unavoidable in| 
practice owing to the nature of the objects. There t 
may be objects in which the dividing characters 
are not distinctly marked, objects that possess the 
differentiae of more than one group in a greater or less 
degree. Things are not always marked off from one 
another by hard and fast lines. They shade into 
one another by imperceptible gradations. A clear 
separation of them may be impossible. In that case 
you must allow a certain indeterminate margin between 



96 Definition. 

your classes, and sometimes it may be necessary to 
put an object into more than one class. 

To insist that there is no essential difference unless 
a clear demarcation can be made is a fallacy. A 
sophistical trick called the Sorites or Heap from the 
classical example of it was based upon this difficulty 
of drawing sharp lines of definition. Assuming that 
it is possible to say how many stones constitute a 
heap, you begin by asking whether three stones form 
a heap. If your respondent says No, you ask whether 
four stones form a heap, then five, and so oa and he 
is puzzled to say when the addition of a single stone 
makes that a heap which was not a heap before Or 
you may begin by asking whether twenty stones form 
a heap, then nineteen, then eighteen, and so on, the 
difficulty being to say when what was a heap ceases 
to be so. 

Where the objects classified are mixed states oi 
affections, the products of interacting factors, ot 
differently interlaced or interfused growths from 
common roots, as in the case of virtues, or emotions, 
or literary qualities, sharp demarcations are impossible. 
To distinguish between wit and humour, or humour 
and pathos, or pathos and sublimity is difficult because 
the same composition may partake of more than one 
character. The specific characters cannot be made 
rigidly exclusive one of another. 

Even in the natural sciences, where the individuals 
are concrete objects of perception, it may be difficult 
to decide in which of two opposed groups an object 
should be included. Sydney Smith has commemorated 
the perplexities of Naturalists over the newly dis- 
covered animals and plants of Botany Bay, in especial 
with the OmithorynchuSy — *' a quadruped as big as a 



Fixation of Meaning. 97 

large cat, with the eyes, colour, and skin of a mole, 
and the bill and web-feet of a duck — puzzling Dr. 
Shaw, and rendering the latter half of his life miser- 
able, from his utter inability to determine whether it 
was a bird or a beast ". 

III. The classes in any scheme of division should \ 
be of co-ordinate rank. 

The classes may be mutually exclusive, and yet the \ 
division imperfect, owing to their not being of equal J 
rank. Thus in the ordinary division of the Parts of 
Speech, parts, that is, of a sentence, Prepositions and 
Conjunctions are not co-ordinate in respect of function, 
which is the basis of the division, with Nouns, Adjec- 
tives, Verbs, and Adverbs. The preposition is a part 
of a phrase which serves the same function as an 
adjective, e,g,^ royal army, army of the king ; it is thus 
functionally part of a part, or a particle. So with the 
conjunction : it also is part of a part, /.^., part of a 
clause serving the function of adjective or adverb. 

IV. The basis of division (Jundamentum divisionis) 
should be an attribute admitting of important 
differences. 

The importance of the attribute chosen as basis may 
vary with the purpose of the division. An attribute 
that is of no importance in one division, may be 
important enough to be the basis of another division. 
Thus in a division of houses according to their archi- 
tectural attributes, the number of windows or the rent 
is of little importance ; but if houses are taxed or rated 
according to the number of windows or the rent, these 
attributes become important enough to be a basis of 
division for purposes of taxation or rating. They then 
admit of important differences. 

7 



98 Definition. 

\ That the importance is relative to the purpose of the 
I division should be borne in mind because there is a 
tendency to regard attributes that are of importance 
in any familiar or pre-eminent division as if they had 
an absolute importance. In short, disregard of this 
relativity is a fallacy to be guarded against. 
^ In the sciences, the purpose being the attainment 
\ and preservation of knowledge, the objects of study are 
divided so as to serve that purpose. Groups must be 
formed so as to bring together the objects that have 
most in common. The question, Who are to be placed 
together ? in any arrangement for purposes of study, 
receives the same answer for individuals and for classes 
that have to be grouped into higher classes, namely, 
Those that have most in common. This is what Dr. 
Bain happily calls **the golden rule'' of scientific 
classification : " Of the various groupings of resembling 
things, preference is given to such as have the greatest 
number of attributes in common ". I slightly modify 
Dr. Bain's statement : he says " the most numerous 
and the most important attributes in common ". But 
for scientific purposes number of attributes constitutes 
importance, as is well recognised by Dr. Fowler when 
he says that the test of importance in an attribute pro- 
posed as a basis of classification is the number of 
other attributes of which it is an index or invariable 
accompaniment. Thus in Zoology the squirrel, the 
rat, and the beaver are classed together as Rodents, 
the difference between their teeth and the teeth of 
other Mammalia being the basis of division, because 
the difference in teeth is accompanied by differences in 
many other properties. So the hedge-hog, the shrew- 
mouse, and the mole, though very unlike in outward 
appearance and habits, are classed together as Insec- 



Fixation of Meaning. 9$ 

tivora, the difference in what they feed on being 
accompanied by a number of other differences. 

The Principles (/Definition. The word ** definition " 
as used in Logic shows the usual tendency of words to 
wander from a strict meaning and become ambiguous. 
Throughout most of its uses it retains this much of a 
common signification, the fixing or determining of the 
boundaries of a class* by making clear its constituent 
attributes. Now in this making clear two processes 
may be distinguished, a material process and a verbal 
process. We have (i) the clearing up of the common 
attributes by a careful examination of the objects 
included in the class : and we have (2) the statement 
of these common attributes in language. The rules 
of definition given by Dr. Bain, who devotes a 
separate Book in his Logic to the subject of 
Definition, concern the first of these processes : the 
rules more commonly given concern mainly the 
second. 

One eminent merit in Dr. Bain*s treatment is that 
it recognises the close connexion between Definition 
and Classification. His cardinal rules are reduced to 
two. 



1 Some logicians, however, speak of defining a thing, and 
illustrate this as if by a thing they meant a concrete individual, 
the realistic treatment of Universals lending itself to such 
expressions. But though the authority of Aristotle might be 
claimed for this, it is better to confine the name in strictness to 
the main process of defining a class. Since, however, the method 
is the same whether it is an individual or a class that we want to 
make distinct, there is no harm in the extension of the word 
definition to both varieties. See Davidson*s Logic of Definition^ 
chap. ii. 



loo Definition, 

L Assemble for comparison representaiwe individuals 
of the class. 

11. Assemble for comparison representative individuals 
of the contrasted class or classes. 

Seeing that the contrasted classes are contrasted on 
some basis of division, this is in effect to recognise 
that you cannot clearly define any class except in a 
scheme of classification. You must have a wide genus 
with \\z fundamentum divisionis^ and, within this, species 
distinguished by their several differentioe. 

Next, as to the verbal process, rules are commonly 
laid down mostly of a trifling and obvious character. 
That " a definition should state neither more nor less 
than the common attributes of the class," or than the 
attributes signified by the class-name, is sometimes 
given as a rule of definition. This is really an 
explanation of what a definition is, a definition of a 
definition. And as far as mere statement goes it ii 
not strictly accurate, for when the attributes of a 
genus are known it is not necessary to give all the 
attributes of the species, which include the generic 
attributes as well, but it is sufficient to give the 
generic name and the differentia. Thus Poetry may 
be defined as " a Fine Art having metrical language 
as its instrument". This is technically known as 
definition per genus et differentiam. This mode of 
statement is a recognition of the connexion between 
Definition and Division. 

The rule that " a definition should not be a synony- 
mous repetition of the name of the class to be defined," 
is too obvious to require formal statement. To describe 
a Viceroy as a man who exercises viceregal functions, 
may have point as an epigram in the case of z. faineant 
vicerov. but it is not a definition. 



Fixation of Meaning. loi 

So with the rule that " a definition should not be \ 
couched in ambiguous unfamiliar, or figurative 
language ". To call the camel " the ship of the 
desert" is a suggestive and luminous description of 
a property, but it is not a definition. So with the 
noble description of Faith as "the substance of 
things hoped for, the evidence of things not seen ". 
But if one wonders why so obvious a " rule " should 
be laid down, the answer is that it has its historical 
origin in the caprices of two classes of offenders, 
mystical philosophers and pompous lexicographers.* 

That "the definition should be simply convertible 
with the term for the class defined," so that we may 
say, for example, either: "Wine is the juice of the 
grape," or, "The juice of the grape is wine," is an 
obvious corollary from the nature of definition, but 
nhould hardly be dignified with the name of a " rule ". 

The Principles of Naming, Rules have been formu- 
lated for the choice of names in scientific definition and 
classification, but it may be doubted whether such choice 
can be reduced to precise rule. It is enough to draw 
attention to certain considerations obvious enough on 
reflection. 

We may take for granted that there should be 
distinct names for every defining attribute (a Termi-] 
nology) and for every group or class (a Nomenclature). 
What about the selection of the names ? Suppose an 
investigator is struck with likenesses and differences 
that seem to him important enough to be the basis of 
a new division, how should he be guided in his choice 
of names for the new groups that he proposes ? Should 

* Sec Davidson's Logic of Definition^ chap, iiL 



I09 Definition. 

he coin new names, or should he take old names and 
try to fit them with new definitions ? 

The balance of advantages is probably in favour of 
Dr. Whewell's dictum that " in framing scientific 
terms, the appropriation of old words is preferable to 
the invention of new ones". Only care must be taken 
to keep as close as possible to the current meaning of 
the old word, and not to run counter to strong associa- 
tions. This is an obvious precept with a view to 
avoiding confusion. Suppose, for example, that in 
dividing Governments you take the distribution of 
political power as your basis of division and come to 
the conclusion that the most important differences are 
whether this power is vested in a few or in the 
majority of the community. You want names to fix 
this broad division. You decide instead of coining 
the new word Pollarchy to express the opposite of 
Oligarchy to use the old words Republic and Oligarchy. 
You would find, as Sir George Cornewall Lewis 
found, that however carefully you defined the word 
Republic, a division under which the British Govern- 
ment had to be ranked among Republics would not 
be generally understood and accepted. Using the 
word in the sense explained above, Mr. Bagehot 
maintained that the constitution of Great Britain 
was more Republican than that of the United 
States, but his meaning was not taken except by 
a few. 

The difficulty in choosing between new words and 
old words to express new meanings is hardly felt in 
the exact sciences. It is at least at a minimum. 
The innovator may encounter violent prejudice, but, 
arguing with experts, he can at least make sure of 
being understood, if his new division is based upon 



Fixation of Meaning, 103 

real and important differences. But in other subjects 
the difficulty of transmitting truth or of expressing it 
in language suited for precise transmission, is almost 
greater than the difficulty of arriving at truth. Between 
new names and old names redefined, the possessor of 
fresh knowledge, assuming it to be perfectly verified, 
is in a quandary. The objects with which he deals 
are already named in accordance with loose divisions \ 
resting on strong prejudices. The names in current 
use are absolutely incapable of conveying his meaning. 
He must redefine them if he is to use them. But in 
that case he runs the risk of being misunderstood 
from people being too impatient to master his rede- 
finition. His right to redefine may even be challenged 
without any reference to the facts to be expressed : he 
may simply be accused of circulating false linguistic 
coin, of debasing the verbal currency. The other 
alternative open to him is to coin new words. In 
that case he runs the risk of not being read at all. 
His contribution to verified knowledge is passed by 
as pedantic and unintelligible. There is no simple 
rule of safety : between Scylla and Charybdis the 
mariner must steer as best he may. Practically the 
advantage lies with old words redefined, because | 
thereby discussion is provoked and discussion clears 
the air. 

Whether it is best to attempt a formal definition 
or to use words in a private, peculiar, or esoteric 
sense, and leave this to be gathered by the reader 
from the general tenor of your utterances, is a question 
of policy outside the limits of Logic. It is for the 
logician to expound the method of Definition and the 
conditions of its application : how far there are subjects 
that do not admit of its application profitably must be 



104 Definition. 

decided on other grounds. But it is probably true 
that no man who declines to be bound by a formal 
definition of his terms is capable of carrying them 
in a clear unambiguous sense through a heated 
controversy. 



Chapter II, 

THE FIVE PREDICABLES.— VERBAL AND REAL 
PREDICATION. 

We give a separate chapter to this topic out of respect 
for the space that it occupies in the history of Logic. 
But except as an exercise in subtle distinction for its 
own sake, all that falls to be said about the Predicables 
might be given as a simple appendix to the chapter on 
Definition. 

Primarily, the Five Predicables or Heads of Predi- 
cables — Genus, Species, Differentia, Proprium, and 
Accidens — are not predicables at all, but merely a list 
or enumeration of terms used in dividing and defining 
on the basis of attributes. They have no meaning 
except in connexion with a fixed scheme of division. 
Given such a scheme, and we can distinguish in it 
the whole to be divided (the genus), the subordinate 
divisions (the species), the attribute or combination of 
attributes on which each species is constituted (the 
differentia), and other attributes, which belong to some 
or all of the individuals but are not reckoned for pur- 
poses of division and definition {Propria and Accidentia). 
The list is not itself a logical division : it is hetero- 
geneous, not homogeneous ; the two first are names 
of classes, the three last of attributes. But correspond- 
ing to it we might make a homogeneous division of 
attributes, as follows: — 

(ios) 



io6 Definition. 



V 


Attributes 

1 






Defining 


Non-defining 

1 




Generic 


1 

Specific 

(Differentia) 


Proprium 


Accidens 



The origin of the title Predicables as applied to these 
five terms is curious, and may be worth noting as an 
instance of the difficulty of keeping names precise, and 
of the confusion arising from forgetting the purpose 
of a name. Porphyry in his cto-aywy^ or Introduction 
explains the five words (<^a)vat) simply as terms that it is 
useful for various purposes to know, expressly mention- 
ing definition and division. But he casually remarks 
that Singular names, ** This man,*' " Socrates," can 
be predicated only of one individual, whereas Genera^ 
Species y Differentice, etc., are predicable of many. That 
is to say he describes them as Predicables simply by 
contradistinction from Singular names. A name, 
however, was wanted for the five terms taken all 
together, and since they are not a logical division, but 
merely a list of terms used in dividing and defining, 
there was no apt general designation for them such 
as would occur spontaneously. Thus it became the 
custom to refer to them as the Predicables, a means of 
reference to them collectively being desiderated, while 
the meaning of this descriptive title was forgotten. 

To call the five divisional elements or Divisoria 
Predicables is to present them as a division of Predi- 
cate Terms on the basis of their relation to the Subject 
Term : to suggest that every Predicate Term must be 
either a Genus or a Species, or a Differentia, or a 



The Five Predicables, 107 

Proprium, or an Accidens of the Subject Term, They 
are sometimes criticised as such, and it is rightly 
pointed out that the Predicate is never a species of or 
with reference to the Subject. But, in truth, the five 
so-called Predicables were never meant as a division of 
predicates in relation to the subject : it is only the title 
that makes this misleading suggestion. 

To complete the confusion it so happens that Aris- 
totle used three of the Five terms in what was virtually 
a division of Predicates inasmuch as it was a division 
of Problems or Questions. In expounding the methods 
of Dialectic in the Topica he divided Problems into 
four classes according to the relation of the Predicate 
to the Subject. The Predicate must either be simply 
convertible with the subject or not. If simply con- 
vertible, the two must be coextensive, and the Predi- 
cate must be either a Proprium or the Definition. If 
not simply convertible, the Predicate must either be 
part of the Definition or not. If part of the Definition 
it must be either a Generic Property or a Differentia 
(both of which in this connexion Aristotle includes 
under Genus) : if not part of the Definition, it is an 
Accident. Aristotle thus arrives at a fourfold division 
of Problems or Predicates: — y€vo% {Genus ^ including 
Differentia^ 8ta<jf)o/oa) ; opos (Definition) ; to tStov (Pro- 
prium) ; and to (rvfjilie/SrjKos (Accidens). The object of it 
was to provide a basis for his systematic exposition ; 
each of the four kinds admitted of differences in 
dialectic method. For us it is a matter of simple 
curiosity and ingenuity. It serves as a monument of 
how much Greek dialectic turned on Definition, and it 
corresponds exactly to the division of attributes into 
Defining and Non-defining given above. It is some- 
times said that Aristotle showed a more scientific mind 



io8 Definition. 

than Porphyry in making the Predicables four instead 
of five. This is true if Porphyry's list had been meant 
as a division of attributes : but it was not so meant. 

The distinction between Verbal or Analytic and 
fieal or Synthetic Predication corresponds to the 
distinction between Defining and Non-defining attri- 
butes, and also has no significance except with 
reference to some scheme of Division, scientific and 
precise or loose and popular. 

When a proposition predicates of a subject something 
contained in the full notion, concept, or definition of 
the subject term, it is called Verbal, Analytic, or 
Explicative: verbal^ inasmuch as it merely explains 
the meaning of a name; explicative for the same 
reason ; analytic^ inasmuch as it unties the bundle of 
attributes held together in the concept and pays out 
one, or all one by one. 

When the attributes of the Predicate are not contained 
in the concept of the Subject, the proposition is called 
Real^ Synthetic^ or Ampliative^ for parallel reasons. 

Thus : " A triangle is a three-sided rectilinear 
figure " is Verbal or Analytic ; " Triangles have 
three angles together equal to two right angles,'* 
or *' Triangles are studied in schools," is Real or 
Synthetic. 

According to this distinction, predications of the 
whole Definition or of a Generic attribute or of a 
Specific attribute are Verbal : predications of Accident 
are Real. A nice point is whether Propria are Verbal 
or Real. They can hardly be classed with Verbal, 
inasmuch as one may know the full meaning of the 
name without knowing them : but it might be argued 
that they are Analytic, inasmuch as they are implicitly 



Tie Five Fredicables. 109 

contained in the defining attributes as being deducible 
from them. 

Observe, however, that the whole distinction is really 
valid only in relation to some fixed or accepted scheme 
of classification or division. Otherwise, what is Verbal 
or Analytic to one man may be Real or Synthetic to 
another. It might even be argued that every proposi- 
tion is Analytic to the man who utters it and Synthetic 
to the man who receives it. We must make some 
analysis of a whole of thought before paying it out in 
words : and in the process of apprehending the meaning 
of what we hear or read we must add the other members 
of the sentence on to the subject. Whether or not this 
is super-subtle, it clearly holds good that what is 
Verbal (in the sense defined) to the learned man of 
science may be Real to the learner. That the horse 
has six incisors in each jaw or that the domestic dog 
has a curly tail, is a Verbal Proposition to the Natural 
Historian, a mere exposition of defining marks ; but 
the plain man has a notion of horse or dog into which 
this defining attribute does not enter, and to him 
accordingly the proposition is Real. 

But what of propositions that the plain man would 
at once recognise as Verbal ? Charles Lamb, for 
example, remarks that the statement that "a good 
name shows the estimation in which a man is held 
in the world " is a verbal proposition. Where is the 
fixed scheme of division there ? The answer is that 
by a fixed scheme of division we do not necessarily 
mean a scheme that is rigidly, definitely and precisely 
fixed. To make such schemes is the business of 
Science. But the ordinary vocabulary of common 
intercourse as a matter of fact proceeds upon schemes 
of division, though the names used in common speech 



no Definition. 

are not always scientifically accurate, not always the 
best that could be devised for the easy acquisition and 
sure transmission of thorough knowledge. The plain 
man's vocabulary, though often twisted aside by such 
causes as we have specified, is roughly moulded on 
the most marked distinguishing attributes of things. 
This was practically recognised by Aristotle when he 
made one of his modes of definition consist in some- 
thing like what we have called verifying the meaning 
of a name, ascertaining the attributes that it signifies 
in common speech or in the speech of sensible men. 
This is to ascertain the essence, ovo-ta, or Substantia^ 
of things, the most salient attributes that strike the 
common eye either at once or after the closer inspection 
that comes of long companionship, and form the basis 
of the ordinary vocabulary. " Properly speaking," 
Mansel says,^ "All Definition is an inquiry into 
Attributes, Our complex notions of Substances can 
only be resolved into various Attributes, with the 
addition of an unknown substratum: a something to 
which we are compelled to regard these attributes 
as belonging. Man^ for example, is analysed into 
Animality, Rationality, and the something which 
exhibits these phenomena. Pursue the analysis and 
the result is the same. We have a something 
corporeal, animated, sensible, rational. An unknown 
constant must always be added to complete the 
integration." This "unknown constant" was what 
Locke called the Real Essence, as distinguished from 
the Nominal Essence, or complex of attributes. It 

1 Aldrich's Compendium, Appendix, Note C. The reader may 
be referred to Mansel's Notes A and C for valuable historical 
notices of the Prcdicables and Definition. 



The Five Predicables. iii 

is upon this nominal essence, upon divisions of things 
according to attributes, that common speech rests, 
and if it involves many cross-divisions, this is 
because the divisions have been made for limited 
and conflicting purposes. 



Chapter IIL 

ARISTOTLE'S CATEGORIESe 

In deference to tradition a place must be found in 
every logical treatise for Aristotle's Categories. No 
writing of the same length has exercised a tithe of its 
influence on human thought. It governed scholastic \ 
thought and expression for many centuries, being from 
its shortness and consequent easiness of transcription 
one of the few books in every educated man's library. 
It still regulates the subdivisions of Parts of Speech in 
our grammars. Its universality of acceptance is shown 
in the fact that the words category {KaTrjyopta) and Jfre- 
dicamenty its Latin translation, have passed into 
common speech. 

The Categories have been much criticised and often 
condemned as a division, but, strange to say, few have 
inquired what they originally professed to be a division 
of, or what was the original author's basis of division. 
Whether the basis is itself important, is another 
question : but to call the division imperfect, without 
reference to the author's intention, is merely confusing, 
and serves only to illustrate the fact that the same 
objects may be differently divided on different principles 
of division. Ramus was right in saying that the 
Categories had no logical significance, inasmuch as 

(112) 



Aristotle's Categories. 113 

they could not be made a basis for departments of 
logical method ; and Kant and Mill in saying that they 
had no philosophical significance, inasmuch as they are 
founded upon no theory of Knowing and Being : but 
this is to condemn them for not being what they were 
never intended to be. 

The sentence in which Aristotle states the objects to 
be divided, and his division of them is so brief and bold 
that bearing in mind the subsequent history of the 
Categories, one first comes upon it with a certain 
surprise. He says simply : — 

'*0f things expressed without syntax {U., single 
words), each signifies either substance, or quantity, or 
quality, or relation, or place, or time, or disposition 
(/.^., attitude or internal arrangement), or appurtenance, 
or action (doing), or suffering (being done to)." ^ 

The objects, then, that Aristotle proposed to classify! 
were single words (the themata simplicia of the School- 
men). He explains that by ** out of syntax " (dvci 
G-vfXTrXoKrjs) he means without reference to truth or 
falsehood: there can be no declaration of truth or 
falsehood without a sentence, a combination, or syntax : 
**man runs'' is either true or false, "man" by itself, 
" runs '^ by itself, is neither. His division, therefore,' 
was a division of single words according to their dif- 
ferences of signification, and without reference to the 
truth or falsehood of their predication.2 

Signification was thus the basis of division. But { 

«X«»'» ^ woieTv, ^ irdtrxeiy. (Categ. ii. 6.) 

»To describe the Categories as a grammatical division, as 
Mansel does m his instructive Appendix C to Aldrich, is a little 
misleadmg without a qualification. They are non-logical inas* 

o 



1 14 DefinmoH, 

according to what differences ? The Categories them- 
selves are so abstract that this question might be 
discussed on their bare titles interminably. But often 
when abstract terms are doubtful, an author's intention 
may be gathered from his examples. And when Aris- 
totle's examples are ranged in a table, certain principles 
of subdivision leap to the eyes. Thus : — 

much as they have no bearing on any logical purpose. But they 
are grammatical only in so far as they are concerned with words. 
They are not grammatical in the sense of being concerned with 
the function of words in predication. The unit of grammar in 
this sense is the sentence, a combination of words in syntax ; and 
it is expressly with words out of syntax that Aristotle deals, with 
single words not in relation to the other parts of a sentence, but in 
relation to the things signified. In any strict definition of the 
provinces of Grammar and Logic, the Categories are neither 
grammatical nor logical: the grammarians have appropriated 
them for the subdivision of certain parts of the sentence, but with 
no more right than the logicians. They really form a treatise by 
themselves, which is in the main ontological, a discussion of sub- 
stances and attributes as underlying the forms of common speech. 
In saying this I use the word substance in the modern sense : but 
it must be remembered that Aristotle's oxxrUj translated substantia, 
covered the word as well as the thing signified, and that his 
Categories are primarily classes of words. The union between 
names and things would seem to have been closer in the Greek 
mind than we can now realise. To get at it we must note that 
every separate word {rh XcyS/xfvoy) is conceived as having a being 
or thing {rh 6y) corresponding to it, so that beings or things 
(tA 6yra) are coextensive with single words : a being or thing is 
whatever receives a separate name. This is clear and simple 
enough, but perplexity begins when we try to distinguish between 
this nameable being and concrete being, which last is Aristotle's 
category of ova-ta, the being signified by a Proper or a Common 
as distinguished from an Abstract Noun. As we shall see, it is 
relatively to the highest sense of this last kind of being, namely, 
the being signified by a Proper name, that he considers the other 
kinds of being. 



Aristotle's Categories, 



•«S 



Substance 


Man 


Common 


Substance 


(o^crfe) 


(oytfpctwros) 


Noun 




{Substantia) 








Quantity 


Five-feet-live 




^ 


{ttoctov) 


(rptTnyxv) 






(Quantitas) 




> 


Permanent 


Quality 


Scholarly 


I 




{iroLov) 


{ypafifiariKOv) 


o 




{Qualitas) 




H 




Relation 


Bigger 


W 


Attribute 


(TTpds Tl) 


Qi€iCov) 






{Relatio) 


' 




b 


Place 


In-the-LyceuniN 




r 


(ttoS) 


(cF AvK€L<a) 


> 




{Ubi) 








Time 


Yesterday 




Temporary 


(ttot^ 


w«) 


(0 




{Quando) 


< 






Disposition 


Reclines . 






(K€tcr^at) 


(dva/ccirai) 






\Positio) 




^ 




Appurtenance 


Has-shoes-on 






(lx«r) 


(wo8€8€T<u) 






{Habitus) 




. ^ 




Action 


Cuts 


3 


Attribute 


(TTOtCtv) 


(t€/XV€i) 






{Actio) 








Passion 


Is cut 






(7ra(7X€fcv) 


(rc/AVCTOt) 




\ 


(/bw/i?) 









In looking at the examples, our first impression 
is that Aristotle has fallen into a confusion. He 
f)rofesses to classify words out of syntax, yet he 



ii6 Definftton. 

gives words with the marks of syntax on them. 
\ Thus his division is accidentally grammatical, a 
division of parts of speech, parts of a sentence, 
into Nouns, Adjectives, Adverbs, and Verbs. And 
his subdivisions of these parts are still followed in 
our grammars. But really it is not the grammatical 
function that he attends to, but the signification : 
and looking further at the examples, we see what 
differences of signification he had in his mind. It 
is differences relative to a concrete individual, 
differences in the words applied to him according 
as they signify the substance of him or his attributes, 
permanent or temporary. 

Take any concrete thing, Socrates, this book, this 
table. It must be some kind of a thing, a man, a 
book. It must have some size or quantity, six feet 
high, three inches broad. It must have some quality, 
white, learned, hard. It must have relations with 
other things, half this, double that, the son of a 
father. It must be somewhere, at some time, in 
some attitude, with some "havings," appendages, 
appurtenances, or belongings, doing something, or 
having something done to it. Can you conceive any 
name (simple or composite) applicable to any object 
of perception, whose signification does not fall into 
one or other of these classes ? If you cannot, the 
categories are justified as an exhaustive division of 
significations. They are a complete list of the most 
general resemblances among individual things, in 
other words, of the summa genera^ the genera general- 
issima of predicates concerning this, that or the 
other concrete individual. No individual thing is 
sui generis: everything is like other things; the 
categories are the most general likenesses. 



Aristotle^ s Categories. 117 

The categories are exhaustive, but do they fulfil 
another requisite of a good division — are they mutually 
exclusive ? Aristotle himself raised this question, and 
some of his answers to difficulties are instructive. 
Particularly his discussion of the distinction between 
Second Substances or Essences and Qualities. Here 
he approximates to the modern doctrine of the distinc- 
tion between Substance and Attribute as set forth in 
our quotation from Mansel at p. no. Aristotle's 
Second Essences (Scvre/oai ova-Lai) are common nouns 
or general names, Species and Genera, man, horsCy 
animal^ as distinguished from Singular names, this 
man, this horse^ which he calls First Substances (Trpcorat 
ovo-tat), essences par excellence, to which real existence in 
the highest sense is attributed. Common nouns are put 
in the First Category because they are predicated in 
answer to the question, What is this ? But he raises 
the difficulty whether they may not rather be regarded 
as being in the Third Category, that of Quality (to 
iroiQv). When we say, "This is a man," do we not 
declare what sort of a thing he is ? do we not declare 
his Quality ? If Aristotle had gone farther along 
this line, he would have arrived at the modern point 
of view that a man is a man in virtue of his possessing 
certain attributes, that general names are applied in 
virtue of their connotation. This would have been 
to make the line of distinction between the First 
Category and the Third pass between First Essence 
and Second, ranking the Second Essences with 
Qualities. But Aristotle did not get out of the 
difficulty in this way. He solved it by falling back 
on the differences in common speech. " Man " does 
not signify the quality simply, as " whiteness " does. 
** Whiteness " signifies nothing but the quality. That 



ii8 Definition. 

is to say, there is no separate name in common 
speech for the common attributes of man. His 
further obscure remark that general names "define 
quality round essence " (^€pi ovcrtW), inasmuch as 
they signify what sort a certain essence is, and that 
genera make this definition more widely than species, 
bore fruit in the mediaeval discussions between Realists 
and Nominalists by which the signification of general 
names was cleared up. 

Another difficulty about the mutual exclusiveness of 
the Categories was started by Aristotle in connexion 
with the Fourth Category, Relation (^rpos ti Adaliquid^ 
To something). Mill remarks that " that could not be 
a very comprehensive view of the nature of Relation 
which would exclude action, passivity, and local situation 
from that Category," and many commentators, from 
Simplicius down to Hamilton, have remarked that all 
the last six Categories might be included under Rela- 
tion. This is so far correct that the word Relation is one 
of the vaguest and most extensive of words ; but the 
criticism ignores the strictness with which Aristotle 
confined himself in his Categories to the forms of 
common speech. It is clear from his examples that in 
his Fourth Category he was thinking only of *^ relation " 
as definitely expressed in common speech. In his 
meaning, any word is a relative which is joined with 
another in a sentence by means of a preposition or 
a case-inflection. Thus " disposition " is a relative : 
it is the disposition of something. This kind of 
relation is perfect when the related terms reciprocate 
grammatically ; thus " master," " servant," since we 
can say either " the master of the servant," or " the 
servant of the master ". In mediaeval logic the term 
Relata was <^nfined to these perfect cases, but the 



Aristotle's Categories. ng 

Category had a wider scope with Aristotle. And he 
expressly raised the question whether a word might 
not have as much right to be put in another Category 
as in this. Indeed, he went further than his critics 
in his suggestions of what Relation might be made 
to include. Thus: "big" signifies Quality; yet a 
thing is big with reference to something else, and ia 
so far a Relative. Knowledge must be knowledge oi 
something, and is a relative : why then should we put 
"knowing" (/.^., learned) in the Category of Quality. 
"Hope" is a relative, as being the hope of a man and 
the hope of something. Yet we say, " I have hope," 
and there hope would be in the category of Having, 
Appurtenance. For the solution of all such difficulties, 
Aristotle falls back upon the forms of common speech, 
and decides the place of words in his categories 
according to them. This was hardly consistent with 
his proposal to deal with separate words out of syntax, 
if by this was meant anything more than dealing with 
them without reference to truth or falsehood. He did 
not and could not succeed in dealing with separate 
words otherwise than as parts of sentences, owing 
their signification to their position as parts of a transient 
plexus of thought. In so far as words have their being 
in common speech, and it is their being in this sense 
that Aristotle considers in the Categories, it is a 
transient being. What being they represent besides is, 
in the words of Porphyry, a very deep affair, and one 
that needs other and greater investigation. 



Chapter IV, 

THE CONTROVERSY ABOUT UNIVERSALS.— DIFFL 
CULTIES CONCERNING THE RELATION OF 
GENERAL NAMES TO THOUGHT AND TO 
REALITY. 

In the opening sentences of his Isagoge, before giving 
^ his simple explanation of the Five Predicables, 
! Porphyry mentions certain questions concerning 
Genera and Species, which he passes over as being 
too difficult for the beginner. '* Concerning genera and 
species," he says, " the question whether they subsist 
(/.^., have real substance), or whether they lie in the 
mere thoughts only, or whether, granting them to sub- 
sist, they are corporeal or incorporeal, or whether they 
subsist apart, or in sensible things and cohering round 
them-— this I shall pass over, such a question being a 
very deep affair and one that needs other and greater 
investigation." 

This passage, written about the end of the third 
century, a.d., is a kind of isthmus between Greek 
Philosophy and Mediaeval : it summarises questions 
which had been turned over on every side and most 
intricately discussed by Plato and Aristotle and their 
successors, and the bald summary became a starting- 
point for equally intricate discussions among the 
Schoolmen, among whom every conceivable variety of 
doctrine found champions. The dispute became known 

(i2o) 



The Controversy about Universals. lai 

as the dispute about Universals, and three ultra- 
typical forms of doctrine were developed, known 
respectively as Realism, Nominalism, and Concep- 
tualism. Undoubtedly the dispute, with all its waste 
of ingenuity, had a clearing effect, and we may fairly 
try now what Porphyry shrank from, to gather some 
simple results for the better understanding of general 
names and their relations to thoughts and to things. 
The rival schools had each some aspect of the general 
name in view, which their exaggeration served to 
render more distinct. 

What does a general name signify? For logical 
purposes it is sufficient to answer — the points of 
resemblarice as grasped in the mind, fixed by a name 
applicable to each of the resembling individuals. This 
is the signification of the general name logically^ its 
connotation or concept, the identical element of 
objective reference in all uses of a general name. 

But other questions may be asked that cannot be so 
simply answered. What is this concept in thought ? 
What is there in our minds corresponding to the 
general name when we utter it ? How is its significa- 
tion conceived? What is the signification psycho- 
logically f 

We may ask, further. What is there in nature that i 
the general name signifies ? What is its relation to 
reality ? What corresponds to it in the real world ? 
Has the unity that it represents among individuals no 
existence except in the mind ? Calling this unity, this 
one in the many, the Universal {Universale^ to irav), 
what is the Universal ontologically f 

It was this ontological question that was so hotly 
and bewilderingly debated among the Schoolmen. 
Before giving the ultra-typical answers to it, it may be 



132 Definition. 

well to note how this question was mixed up with still 
other questions of Theology and Cosmogony. Recog- 
\ nising that there is a unity signified by the general 
name, we may go on toTnquire into the ground of the 
unity. Why are things essentially like one another ? 
How is the unity maintained ? How is it continued ? 
Where does the common pattern come from? The 
question of the nature of the Universal thusjinks itself 
with metaphysical theories of the construction of the 
world, or even with the Darwinian theory of the origin 
of species. 

Passing by these remoter questions, we may give 
the answers of the three extreme schools to the onto- 
logical question, What is a Universal? 

The answer of the Ultra -Realists, broadly put, was 
that a Universal is a substance having an independent 
existence in nature. 

Of the Ultra-Nominalists, that the Universal is a 
name and nothing else, vox et praterea nihil ; that 
this name is the only unity among the individuals of 
a species, all that they have in common. 

Of the Ultra-Conceptualists, that the individuals 

have more in common than the name, that they have 

the name plus the meaning, vox + signification but that 

the Universals, the genera and species, exist only in 

the mind. 

i Now these extreme doctrines, as literally interpreted 

/ by opponents, are so easily refuted and so manifestly 

' untenable, that it may be doubted whether they were 

ever held by any thinker, and therefore I call them 

Ultra-Realism, Ultra-Nominalism, and Ultra-Concep- 

tualism. They are mere exaggerations or caricatures, 

set up by opponents because they can be easily knocked 

down. 



JS(f Contrmersy about Universals, i«3 

To the Ultra-Realists, it is sufficient to say that if 
there existed anywhere a substance having all the 
common attributes of a species and only these, having 
none of the attributes peculiar to any of the individuals 
of that species, corresponding to the general name as 
an individual corresponds to a Proper or Singular 
name, it would not be the Universal, the unity 
pervading the individuals, but only another individual. 

To the Ultra-Nominalists, it is sufficient to say that 
the individuals must have more in common than the 
name, because the name is not applied arbitrarily, 
but on some ground. The individuals must have in 
common that on account of which they receive the 
common name : to call them by the same name is | 
not to make them of the same species. \ 

To the Ultra-Conceptualists, it is sufficient to say 
that when we employ a general name, as when we say 
** Socrates is a man," we do not refer to any passing 
thought or state of mind, but to certain attributes 
independent of what is passing in our minds. We 
cannot make a thing of this or that species by merely 
thinking of it as such. 

The ultra-forms of these doctrines are thus easily 
shown to be inadequate, yet each of the three, Realism, 
Nominalism, and Conceptualism, represents a phase 
of the whole truth. 

Thus, take Realism. Although it is not true that 
there is anything in reality corresponding to the 
general name such as there is corresponding to the 
singular name, the general name merely signifying 
attributes of what the singular name signifies, it 
does not follow, as the opponents of Ultra-Realism 
hastily assume, that there is nothing in the real 
world corresponding to the general name. Three 



124 Definition. 

senses may be particularised in which Realism is 
justified. 

\ (i) The points of resemblance from which the 
-concept is formed are as real as the individuals 
themselves. It is true in a sense that it is our 
thought that gives unity to the individuals of a 
class, that gathers the many into one, and so far 
the Conceptualists are right. Still we should not 
gather them into one if they did not resemble one 
another: that is the reason why we think of them 
together: and the respects in which they resemble 
one another are as much independent of us and 
our thinking as the individuals themselves, as much 
beyond the power of our thought to change. We 
must go behind the activity of the mind in unifying 
to the reason for the unification : and the ground of 
unity is found in what really exists. We do not 
confer the unity : we do not make all men or all 
dogs alike: we find them so. The curly tails in a 
thousand domestic dogs, which serve to distinguish 
them from wolves and foxes, are as real as the 
thousand individual domestic dogs. In this sense 
the Aristotelian doctrine, Universalia in re^ expresses 
a plain truth. 

(2) The Platonic doctrine, formulated by the School- 
men as Universalia ante rem^ has also a plain validity. 

I Individuals come and go, but the type, the Universal, 
is more abiding. Men are born and die : man remains 
throughout. The snows of last year have vanished, 
but snow is still a reality to be faced. Wisdom does 
not perish with the wise men of any generation. In 
this plain sense, at least, it is true that Universals exist 
before Individuals, have a greater permanence, or, if we 
like to say so, a higher, as it is a more enduring, reality. 



Tke Controversy about Universals, 125 

(3) Further, the ** idea," concept, or universal, 
though it cannot be separated from the individual, 
and whether or not we ascribe to it the separate 
suprasensual existence of the archetypal forms of 
Plato's poetical fancy, is a very poteniLfeotor in the 
real world. Ideals of conduct, of manners, of art, of- 
policy, have a traditional life : they do not pass away 
with the individuals in whom they have existed, in 
whom they are temporarily materialised : they survive 
as potent influences from age to age. The " idea " of 
Chaucer's Man of Law, who always " seemed busier 
than he was," is still with us. Mediaeval conceptions 
of chivalry still govern conduct. The Universal enters 
into the Individual, takes possession of him, makes of 
him its temporary manifestation. 

Nevertheless, the Nominalists are right in insisting 
on the importance of names. What we call the real 
world is a common object of perception and knowledge 
to you and me: we cannot arrive at a knowledge of 
it without some means of communication with one 
another: our means of communication is language. 
It may be doubted whether even thinking could go far 
without symbols with the help of which conceptions 
may be made definite. A concept cannot be explained 
without reference to a symbol. There is even a sense 
in which the Ultra-Nominalist doctrine that the indi- 
viduals in a class have nothing in common but the 
name is tenable. Denotability by the same name is the 
only respect in which those individuals are absolutely 
identical : in this sense the name alone is common to 
them, though it is applied in virtue of their resemblance 
to one another. 

Finally, the Conceptualists are right in insisting on 
the mind's activity in connexion with general names. 



It 26 Definmm. 

Genera and species are not mere arbitrary subjective 
collections : the union is determined by the characters 
of the things collected. Still it is with the concept in 
each man's mind that the name is connected : it is by 
the activity of thought in recognising likenesses and 
forming concepts that we are able to master the 
diversity of our impressions, to introduce unity into 
the manifold of sense, to reduce our various recollec- 
tions to order and coherence. 

So much for the Ontological question. Now for the 
Psyohological. What is in the mind when we employ 
a general name ? What is the Universal psychologi- 
cally ? How is it conceived ? 

What breeds confusion in these subtle inquiries is 
the want of fixed unambiguous names for the things to 
be distinguished. It is only by means of such names 
that we can hold on to the distinctions, and keep from 
puzzling ourselves. Now there are three things to be 
distinguished in this inquiry, which we may call the 
Concept, the Conception, and the Conceptual or 
Generic Image. Let us call them by these names, 
and proceed to explain them. 

By the Concept, I understand the meaning of the 
general name, what the general name signifies: by 
the Conception, the mental act or state of him who 
conceives this meaning. The concept of " triangle," 
/.^., what you and I mean by the word, is not my act 
of mind or your act of mind when we think or speak of 
a triangle. The Conception, which is this act, is an 
event or incident in our mental history, a psychical 
act or state, a distinct occurrence, a particular fact in 
time as much as the battle of Waterloo. The concept 
is the objective reference of the name, which is the 
same, or at least is understood to be the same, every 



The Controversy about Universak. lijf 

time we use it. I make a figure on paper with ink 
or on a blackboard with chalk, and recognise or con- 
ceive it as a triangle : you also conceive it as such : 
we do the same to-morrow : we did the same yesterday : 
each act of conception is a different event, but the con- 
cept is the same throughout. 

Now the psychological question about the Universal 
is, What is this conception ? We cannot define it 
positively further than by saying that it consists in 
realising the meaning of a general name : the act 
being unique, we can only make it intelligible by 
producing an example of it But we may define it 
negatively by distinguishing it from the conceptual 
image. Whenever we conceive anything, "man," 
"horse," there is generally present to our minds an 
image of a man or horse, with accidents of size, 
colour, position or other categories. But this concep- 
tual image is not the concept, and the mental act 
of forming it is not conception. 
I This distinction between mental picturing or 
imaging and the conception of common attributes is 
variously expressed. The correlative terms Intuitive 
and Symbolical Thinking, Presentative and Representative 
iCnowledge have been employed.* But whatever terms 



* The only objection to these terms is that they have slipped 
from their moorings in philosophical usage. Thus instead of 
Leibnitz's use of Intuitive and Sjnnbolical, which corresponds 
to the above distinction between Imaging and Conception, Mr. 
Jevons employs the terms to express a distinction among 
conceptions proper. We can understand what a chiliagon 
means, but we cannot form an image of it in our minds, except 
in a very confused and imperfect way; whereas we can form 
a distinct image of a triangle. Mr. Jevons would call the 
conception of the triangle Intuitive^ of the chiliagon SymbolicaL 



128 DefiniticH. 

we use, the distinction itself is vital, and the want of 
it leads to confusion. 

Thus the fact that we cannot form a conceptual 
image composed solely of common attributes has been 
used to support the argument of Ultra-Nominalism, 
that the individuals classed under a common name 
have nothing in common but the name. What the 
word "dog" signifies, Z.^., the "concept" of dog, is 
neither big nor little, neither black nor tan, neithet 
here nor there, neither Newfoundland, nor Retriever, 
nor Terrier, nor Greyhound, nor Pug, nor Bulldog. 
The concept consists only of the attributes common 
to all dogs apart from any that are peculiar to any 
variety or any individual. Now we cannot form any 
such conceptual image. Our conceptual image is 
always of some definite size and shape. Therefore, 
it is argued, we cannot conceive what a dog means, 
and dogs have nothing in common but the name. 
This, however, does not follow. The concept is not 
the conceptual image, and forming the image is not 
conception. We may even, as in the case of a 
chiliagon, or thousand-sided figure, conceive the 
meaning without being able to form any definite 
image. 

How, then, do we ordinarily proceed in conceiving, 
if we cannot picture the common attributes alone and 
apart from particulars ? We attend, or strive to attend, 
only to those aspects of an image which it has in 
common with the individual things denoted. And if 

Again, while Mansel uses the words Presentative and Representa- 
tive to express our distinction, a more common usage is to call 
actual Perception Presentative Knowledge, and ideation or 
recollection in idea Representative. 



The Controversy about Universats. 129 

we want to make our conception definite, we pass in 
review an indefinite number of the individuals, case 
after case. 

A minor psychological question concerns the nature 
of the conceptual image. Is it a copy of some 
particular impression, or a confused blur or blend of 
many ? Possibly neither : possibly it is something 
like one of Mr. Galton's composite photographs, 
photographs produced by exposing the same surface 
to the impressions of a number of different photographs 
in succession. If the individuals are nearly alike, the 
result is an image that is not an exact copy of any 
one of the components and yet is perfectly distinct. 
Possibly the image that comes into our mind's eye 
when we hear such a word as " horse " or ** man " 
is of this character, the result of the impressions of a 
number of similar things, but not identical with any 
one. As, however, different persons have different 
conceptual images of the same concept, so we may 
have different conceptual images at different times. 
It is only the concept that remains the same. 

But how, it may be asked, can the concept remain 
the same ? If the universal or concept psychologically 
is an intellectual act, repeated every time we conceive, 
what guarantee have we for the permanence of the 
concept ? Does this theory not do away with all 
possibility of defining and fixing concepts ? 

This brings us back to the doctrine already laid 
down about the truth of Realism. The theory of the 
concept is not exhausted when it is viewed only 
psychologically, as a psychic act. If we would 
understand it fully, we must consider the act in its 
relations to the real experience of ourselves and 
others. To fix this act, we give it a separate name, 

9 



130 Definiiion, 

calling It the conception : and then we must go behind 
the activity of the mind to the objects on which it is 
exercised. The element of fixity is found in them. 
And here also the truth of Nominalism comes in. 
By means of words we enter into communication 
with other minds. It is thus that we discover what 
is real, and what is merely personal to ourselves* 



PART III. 

THE INTERPRETATION OF PROPOSITIONS. 

—OPPOSITION AND IMMEDIATE 

INFERENCE. 



Chapter I. 



THEORIES OF PREDICATION.—THEORIES OF 
JUDGMENT. 

We may now return to the Syllogistic Forms, and the 
consideration of the compatibility or incompatibility, 
implication, and interdependence of propositions. 

It was to make this consideration clear and simple 
that what we have called the Syllogistic Form of 
propositions was devised. When are propositions 
incompatible ? When do they imply one another ? 
When do two imply a third ? We have seen in the 
Introduction how such questions were forced upon 
Aristotle by the disputative habits of his time. It 
was to facilitate the answer that he analysed 
propositions into Subject and Predicate, and viewed 
the Predicate as a reference to a class : in other words, 
analysed the Predicate further into a Copula and a 
Class Term. 



132 The Interpretation of Propositions. 

But before showing how he exhibited the inter- 
connexion of propositions on this plan, we may turn 
aside to consider various so-called Theories of Predica- 
tion or of Judgment. Strictly speaking, they are not 
altogether relevant to Logic, that is to say, as a 
practical science : they are partly logical, partly 
psychological theories : some of them have no bearing 
whatever on practice, but are matters of pure scientific 
curiosity : but historically they are connected with the 
logical treatment of propositions as having been 
developed out of this. 

The least confusing way of presenting these theories 
is to state them and examine them both logically and 
psychologically. The logical question is. Has the 
view any advantage for logical purposes? Does it 
help to prevent error, to clear up confusion ? Does 
it lead to firmer conceptions of the truth ? The 
psychological question is, Is this a correct theory of 
how men actually think when they make propositions ? 
It is a question of what is in the one case, and of 
what ought to be for a certain purpose in the other. 

Whether we speak of Proposition or of Judgment 
does not materially affect our answer. A Judgment is 
the mental act accompanying a Proposition, or that 
may be expressed in a proposition and cannot be 
expressed otherwise : we can give no other intelligible 
definition or description of a judgment. So a proposi- 
tion can only be defined as the expression of a judg- 
ment : unless there is a judgment underneath them, a 
form of words is not a proposition. 

Let us take, then, the different theories in turn. We 
shall find that they are not really antagonistic, but 
only different : that each is substantially right from its 
own point of view : and that they seem to contradict 



Theories of Predication, 133 

one another only when the point of view is misunder- 
stood. 

I. That the Predicate term may be regarded as a class \ 
in or from which the Subject is included or excluded. \ 
Known as the Class-Inclusion, Class- Reference, or 
Denotative view. 

This way of analysing propositions is possible, as we 
have seen, because every statement implies a general 
name, and the extension or denotation of a general 
name is a class defined by the common attribute or 
attributes. It is useful for syllogistic purposes: 
certain relations among propositions can be most f 
simply exhibited in this way. I 

But if this is called a Theory of Predication or 
Judgment, and taken psychologically as a theory of 
what is in men's minds whenever they utter a 
significant Sentence, it is manifestly wrong. When 
discussed as such, it is very properly rejected. When 
a man says " P struck Q," he has not necessarily a 
class of " strikers of Q '* definitely in his mind. What 
he has in his mind is the logical equivalent of this, but 
it is not this directly. Similarly, Mr. Bradley would 
be quite justified in speaking of Two Terms and a 
Copula as a superstition, if it were meant that these 
analytic elements are present to the mind of an 
ordinary speaker. 

II. That every Proposition may be regarded as affirm^ \ 
ing or denying an attribute of a subject. Known some- / 
times as the Connotative or the Denotative-Connotative 
view. This also follows from the implicit presence of 
a general name in every sentence. But it should not 
be taken as meaning that the man who says: **Tom 
came here yesterday," or ** James generally sits there," 
has a clearly analysed Subject and Attribute in his 



134 ^^ Interpretation of Propositions. 

mind. Otherwise it is as far wrong as the other 
view. 

\ III. TTiat every proposition may be regarded as an 
equation between two terms. Known as the Equational 
View. 

This is obviously not true for common speech or 
ordinary thought. But it is a possible way of regarding 
the analytic components of a proposition, legitimate 
enough if it serves any purpose. It is a modification 
of the Class- Reference analysis, obtained by what is 
known as Quantification of the Predicate, In " All S 
is in P," P is undistributed, and has no symbol of 
Quantity. But since the proposition imports that 
All S is a part of P, i.e.j Some P, we may, if we 
choose, prefix the symbol of Quantity, and then the 
proposition may be read "All S » Some P". And 
so with the other forms. 

Is there any advantage in this ? Yes : it enables 
us to subject the formulae to algebraic manipulation. 

! But any logical advantage — any help to thinking ? 

: None whatever. The elaborate syllogistic systems of 
Boole, De Morgan, and Jevons are not of the slightest 
use in helping men to reason correctly. The value 
ascribed to them is merely an illustration of the Bias 
of Happy Exercise. They are beautifully ingenious, 
but they leave every recorded instance of learned 
Scholastic trifling miles behind. 

j IV. Tfiat every proposition is the expression of a 

\ comparison between concepts. Sometimes called the 
Conceptualist View. 

"To judge," Hamilton says, " is to recognise the 
relation of congruence or confliction in which two 
concepts, two individual things, or a concept and an 
individual compared together stand to each other." 



Theories of Predication. 135 

This way of regarding propositions is permissible or 
not according to our interpretation of the words 
"congruence" and " confliction," and the word 
"concept". If by concept we mean a conceived 
attribute of a thing, and if by saying that two concepts 
are congruent or conflicting, we mean that they may 
or may not cohere in the same thing, and by saying 
that a concept is congruent or conflicting with an 
individual that it may or may not belong to that 
individual, then the theory is a corollary from 
Aristotle's analysis. Seeing that we must pass 
through that analysis to reach it, it is obviously not 
a theory of ordinary thought, but of the thought of a 
logician performing that analysis. 

The precise point of Hamilton's theory was that the 
logician does not concern himself with the question 
whether two concepts are or are not as a matter of 
fact found in the same subject, but only with the 
question whether they are of such a character that 
they may be found, or cannot be found, in the same 
subject. In so far as his theory is sound, it is an 
abstruse and technical way of saying that we may 
consider the consistency of propositions without 
considering whether or not they are true, and that 
consistency is the peculiar business of syllogistic logic. 

V. That the ultimate subject of every judgment is reality. 

This is the form in which Mr. Bradley and Mr. 
Bosanquet deny the Ultra-Conceptualist position. 
The same view is expressed by Mill when he says that 
" propositions are concerned with things and not with 
our ideas of them '\ 

The least consideration shows that there is justice 
in the view thus enounced. Take a number of propo- 
sitions : — 



136 The Interpretation of Propositions. 

The streets are wet. 

George has blue eyes. 

The Earth goes round the Sun. 

Two and two make four. 

Obviously, in any of these propositions, there is a 
reference beyond the conceptions in the speaker's mind, 
viewed merely as incidents in his mental history. 
They express beliefs about things and the relations 
among things in rerum natura : when any one under- 
stands them and gives his assent to them, he never 
stops to think of the speaker's state of mind, but of 
what the words represent. When states of mind 
are spoken of, as when we say that our ideas are 
confused, or that a man's conception of duty influences 
his conduct, those states of mind are viewed as 
objective facts in the world of realities. Even when 
we speak of things that have in a sense no reality, as 
when we say that a centaur is a combination of man 
and horse, or that centaurs were fabled to live in the 
vales of Thessaly, it is not the passing state of mind 
expressed by the speaker as such that we attend to or 
think of; we pass at once to the objective reference of 
the words. 

Psychologically, then, the theory is sound : what is 
its logical value ? It is sometimes put forward as if it 
were inconsistent with the Class-reference theory or 
the theory that judgment consists in a comparison of 
concepts. Historically the origin of its formal state- 
ment is its supposed opposition to those theories. But 
really it is only a misconception of them that it contra- 
dicts. It is inconsistent with the Class-reference view 
only if by a class we understand an arbitrary subjective 
collection, not a collection of things on the ground pf 



Theories of Predication. 137 

common attributes. And it is inconsistent with the 
Conceptualist theory only if by a concept we understand 
not the objective reference of a general name, but what 
we have distinguished as a conception or a conceptual 
image. The theory that the ultimate subject is reality 
is assumed in both the other theories, rightly under- 
stood. If every proposition is the utterance of a 
judgment, and every proposition implies a general 
name, and every general name has a meaning or con- 
notation, and every such meaning is an attribute of 
things and not a mental state, it is implied that 
the ultimate subject of every proposition is reality. 
But we may consider whether or not proposi- 
tions are consistent without considering whether 
or not they are true, and it is only their 
mutual consistency that is considered in the syllo- 
gistic formulae. Thus, while it is perfectly correct 
to say that every proposition expresses either truth or 
falsehood, or that the characteristic quality of a judg- 
ment is to be true or false, it is none the less correct to 
say that we may temporarily suspend consideration of 
truth or falsehood, and that this is done in what is 
commonly known as Formal Logic. 

VI. That every proposition may be regarded as f 
expressing relations between phenomena. 

Bain follows Mill in treating this as the final 
import of Predication. But he indicates more 
accurately the logical value of this view in speaking 
of it as important for laying out the divisions of 
Inductive Logic. They differ slightly in their lists 
of Universal Predicates based upon Import in this 
sense — Mill's being Resemblance, Coexistence, Simple 
Sequence, and Causal Sequence, and Bain's being 
Coe^cistence, Succession, and Equality or Inequality. 



138 The Interpretation of Propositions. 

But both lay stress upon Coexistence and Succession, 
and we shall find that the distinctions between Simple 
Sequence and Causal Sequence, and between Repeated 
and Occasional Coexistence, are all-important in the 
Logic of Investigation. But for syllogistic purposes 
the distinctions have no relevance 



Chapter II. 

THE "OPPOSITION" OF PROPOSITIONS.— THE 
INTERPRETATION OF "NO". 

Propositions are technically said to be "opposed" 
when, having the same terms in Subject and Predicate, 
they differ in Quantity, or in Quality, or in both.^ 

^ This is the traditional definition of Opposition from an taxly 
period, though the tradition does not start ifrom Aristotle. With 
him opposition (ayriK€7<rBai) meant, as it still means in ordinary 
speech, incompatibility. The technical meaning of Opposition is 
based on the diagram (given afterwards in the text) known as the 
Square of Opposition, and probably originated in a confused 
apprehension of the reason why it received that name. It was 
called the Square of Opposition, because it was intended to 
illustrate the doctrine of Opposition in Aristotle's sense and the 
ordinary sense of repugnance or incompatibility. What the 
Square brings out is this. If the four forms A E I O are arranged 
symmetrically according as they differ in quantity, or quality, 
or both, it is seen that these differences do not correspond 
symmetrically to compatibility and incompatibility: that pro- 
positions may differ in quantity or in quality without being 
incompatible, and that they may differ in both (as Contradictories) 
and be less violently incompatible than when they differ in one 
only (as Contraries). The original purpose of the diagram was 
to bring this out, as is done in every exposition of it. Hence it 
was called the Square of Opposition. But as a descriptive title 
this is a misnomer : it should have been the Square of Differences 
in Quantity or Quality. This misnomer has been perpetuated by 
appropriating Opposition as a common name for difference in 
Quantity or Quality when the terms are the same and in the same 

(139) 



140 The Interpretation of Propositions. 

The practical question from which the technical 
doctrine has been developed was how to determine 
the significance of contradiction. What is meant by 
giving the answer " No " to a proposition put interro- 
gatively ? What is the interpretation of " No " ? 
What is the respondent committed to thereby ? 

" Have all ratepayers a vote ? " If you answer 
" No,*' you are bound to admit that some ratepayers 
have not. O is the Contradiotory of A. If A is false, 

must be true. So if you deny O, you are bound to 
admit A : one or other must be true : either Some rate- 
payers have not a vote or All have. 

Is it the case that no man can live without sleep ? 
Deny this, and you commit yourself to maintaining 
that Some man, one at least, can live without sleep 

1 is the Contradictory of E ; and vice verscL. 

Contradictory opposition is distinguished from Con- 
trary, the opposition of one Universal to another, of 
A to E and E to A. There is a natural tendency to 
meet a strong assertion with the very reverse. Let it 
be maintained that women are essentially faithless or 
that ** the poor in a lump is bad," and disputants are 
apt to meet this extreme with another, that constancy 
is to be found only in women or true virtue only among 
ihe poor. Both extremes, both A and E, may be false : 
he truth may lie between : Some are, Some not. 

order, and distinguishing it in this sense from Repugnance (Mr 
Incompatibility (Tataretusin Summulas, D e Oppositionibus [1501]^ 
Keynes, The Opposition 0/ Propositions [1887]). Seeing that there 
never is occasion to speak of Opposition in the limited sense 
except in connexion with the Square, there is no real risk oi 
confusion. A common name is certainly wanted in that connexion, 
if only to say that Opposition (in the limited or diagrammatic 
s^se) does not mean incompatibility. 



The ^^ Of position'' of Propositions. 141 

Logically, the denial of A or E implies only the 
admission of O or I. You are not committed to the 
full contrary. But the implication of the Contradictory 
is absolute ; there is no half-way house where the 
truth may reside. Hence the name of Excluded 
Middle is applied to the principle that " Of two Con- 
tradictories one or other must be true : they cannot 
both be false ". 

While both Contraries may be false, they cannot 
both be true. 

It is sometimes said that in the case of Singular 
propositions, the Contradictory and the Contrary 
coincide. A more correct doctrine is that in the case 
of Singular propositions, the distinction is riot needed 
and does not apply. Put the question " Is Socrates 
wise ? *' or " Is this paper white ? " and the answer 
** No'' admits of only one interpretation, provided the 
terms remain the same. Socrates may become foolish, 
or this paper may hereafter be coloured differently, but 
in either case the subject term is not the same about 
which the question was asked. Contrary opposition 
belongs only to general terms taken universally as 
subjects. Concerning individual subjects an attribute 
must be either affirmed or denied simply : there is no 
middle course. Such a proposition as " Socrates is 
sometimes not wise,*' is not a true Singular proposition, 
though it has a Singular term as grammatical subject. 
Logically, it is a Particular proposition, of which the 
subject-term is the actions or judgments of Socrates.* 

1 Cp. Keynes, pt. ii. ch. ii. s. 57. Aristotle laid down the dis- 
tinction between Contrary and Contradictory to meet another 
quibble in contradiction, based on taking the Universal as a whole 
and indivisible subject like an Individual^ of which a given predi- 
cate must be either affirmed or denied. 



142 The Interpretation of Propositions. 

Opposition, in the ordinary sense, is the opposition of 
incompatible propositions, and it was with this only 
that Aristotle concerned himself. But from an early 
period in the history of Logic, the word was extended 
to cover mere differences in Quantity and Quality 
among the four forms A E I O, which differences have 
been named and exhibited symmetrically in a diagram 
known as : The Square of Opposition. 

A Contraries. .^^.„...«..E 









6 N. 

8 X .f 






J 



CO ^•' 'iv. CO 






Q 



I Sub-contraries O 

The four forms being placed at the four corners of 
the Square, and the sides and diagonals representing 
relations between them thus separated, a very pretty 
and symmetrical doctrine is the result. 

Contradictories^ A and O, E and I, differ both in 
Quantity and in Quality. 

Contraries^ A and E, differ in Quality but not in 
Quantity, and are both Universal. 

Sub-contraries^ I and O, differ in Quality but not in 
Quantity, and are both Particular. 



The " Opposition " of Propositions. 143 

Subalternsy A and I, E and O, differ in Quantity but 
not in Quality. 

Again, in respect of concurrent truth and falsehood 
there is a certain symmetry. 

Contradictories cannot both be true, nor can they 
both be false. 

Contraries may both be false, but cannot both be true. 

Sub-contraries may both be true, but cannot both be 
false. 

Subalterns may both be false and both true. If the 
Universal is true, its subalternate Particular is true : 
but the truth of the Particular does not similarly imply 
the truth of its Subalternating Universal. 

This last is another way of saying that the truth of 
the Contrary involves the truth of the Contradictory, 
but the truth of the Contradictory does not imply the 
truth of the Contrary. 

There, however, the symmetry ends. The sides 
and the diagonals of the Square do not symmetrically 
represent degrees of incompatibility, or opposition in 
the ordinary sense. 

There is no incompatibility between two Sub- 
contraries or a Subaltern and its Subalternant. Both 
may be true at the same time. Indeed, as Aristotle 
remarked of I and O, the truth of the one commonly 
implies the truth of the other : to say that some of the 
crew were drowned, implies that some were not, and 
vice versa. Subaltern and Subalternant also are com- 
patible, and something more. If a man has admitted 
A or E, he cannot refuse to admit I or O, the Particular 
of the same Quality. If All poets are irritable, it 
cannot be denied that some are so ; if None is, that 
Some are not. The admission of the Contrary includes 
the admission of the Contradictory. 



144 ^>^ Interpretation of Propositions. 

Consideration of Subalterns, however, brings to 
light a nice ambiguity in Some. It is only when I is 
regarded as the Contradictory of E, that it can properly 
be said to be Subalternate to A. In that case the 
meaning of Some is " not none," /.^., " Some at least". 
But when Some is taken as the sign of Particular 
quantity simply, Z.^., as meaning ** not all," or ** some 
at most," I is not Subalternate to A, but opposed to it 
in the sense that the truth of the one is incompatible 
with the truth of the other. 

Again, in the diagram Contrary opposition is repre- 
sented by a side and Contradictory by the diagonal ; 
that is to say, the stronger form of opposition by the 
shorter line. The Contrary is more than a denial : 
it is a counter-assertion of the very reverse, to ivdvTtov. 
" Are good administrators always good speakers ? " 
" On the contrary, they never are." This is a much 
stronger opposition, in the ordinary sense, than a 
modest contradictory, which is warranted by the 
existence of a single exception. If the diagram were 
to represent incompatibility accurately, the Contrary 
ought to have a longer line than the Contradictory, 
and this it seems to have had in the diagram that 
Aristotle had in mind {JDe Interpret., c. lo). 

It is only when Opposition is taken to mean merely 
difference in Quantity and Quality that there can be 
said to be greater opposition between Contradictories 
than between Contraries. Contradictories differ both 
in Quantity and in Quality : Contraries, in Quality 
only. 

There is another sense in which the Particular 
Contradictory may be said to be a stronger opposite 
than the Contrary. It is a stronger position to take 
up argumentatively. It is easier to defend than a 



The " Opposition " of Propositions, 145 

Contrary. But this is because it offers a narrower 
and more limited opposition. 

We deal with what is called Immediate Inference 
in the next chapter. Pending an exact definition of 
the process, it is obvious that two immediate inferences 
are open under the above doctrines, (i) Granted the 
truth of any proposition, you may immediately infer 
the falsehood of its Contradictory. (2) Granted the 
truth of any Contrary, you may immediately infer the 
truth of its Subaltern.* 



^ I have said that there is little risk of confusion in using the 
word Opposition in its technical or limited sense. There is, 
however, a little. When it is said that these inferences are based 
on Opposition, or that Opposition is a mode of Immediate Infer- 
ence, there is confusion of ideas unless it is pointed out that when 
this is said, it is Opposition in the ordinary sense that is meant. 
The inferences are really based on the rules of Contrary and 
Contradictory Opposition ; Contraries cannot both be true, and 
of Contradictories one or other must be. 



10 



Chapter III. 

THE IMPLICATION OF PROPOSITIONS.— IMMEDIATE 
FORMAL INFERENCE.— EDUCTION. 

The meaning of Inference generally is a subject of 
dispute, and to avoid entering upon debatable ground 
ftt this stage, instead of attempting to define Inference 
generally, I will confine myself to defining what is 
called Formal Inference, about which there is com- 
paratively little difference of opinion. 

Formal Inference then is the apprehension of what 
is implied in a certain datum or admission : the 
derivation of one proposition, called the Conclusion, 
from one or more given, admitted, or assumed pro- 
positions, called the Premiss or Premisses. 

When the conclusion is drawn from one proposition, 
the inference is said to be immediate ; when more than 
one proposition is necessary to the conclusion, the 
mference is said to be mediate. 

Given the proposition, " All poets are irritable," we 
can immediately infer that " Nobody that is not 
irritable is a poet"; and the one admission implies 
the other. But we cannot infer immediately that 
" all poets make bad husbands ". Before we can do 
this we must have a second proposition conceded, 



The Implication of Propositions. 147 

that " All irritable persons make bad husbands '*. 
The inference in the second case is called Mediate.* 

The modes and conditions of valid Mediate Infer- 
ence constitute Syllogism, which is in effect the 
reasoning together of separate admissions. With this 
we shall deal presently. Meantime of Immediate 
Inference. 

To state all the implications of 9 certain form of \ 
proposition, to make explicit all that it implies, is the \ 
same thing with showing what immediate inferences { 
from it are legitimate. Formal inference, in short, is 
the eduction of all that a proposition implies. 

Most of the modes of Immediate Inference formu- 
lated by logicians are preliminary to the Syllogistic 
process, and have no other practical application. The 
most important of them technically is the process 
known as Conversion, but others have been judged 
worthy of attention. 

^Equipollent or Equivalent Forms — Obversion. 

-ffiquipollence or Equivalence (lo-oSvi/a/Ata) is defined 
as the perfect agreement in sense of two propositions 
that differ somehow in expression.^ 

The history of iEquipoIlence in logical treatises 
illustrates two tendencies. There is a tendency on 
the one hand to narrow a theme down to definite and 
manageable forms. But when a useful exercise is 
discarded from one place it has a tendency to break 
out in another under another name. A third tendency 

^ I purposely chose disputable propositions to emphasise the 
fact that Formal Logic has no concern with the truth, but only 
with the interdependence of its propositions. 

' Mark Duncan, ln%U Log,^ si. 5, 1612. 



148 Tlu Interpretation of Propositions. 

may also be said to be specially well illustrated — the 
tendency to change the traditional application of logical 
terms. 

In accordance with the above definition of -^qui- 
pollence or Equivalence, which corresponds with 
ordinary acceptation, the term would apply to all cases 
of " identical meaning under difference of expression ". 
Most examples of the reduction of ordinary speech 
into syllogistic form would be examples of aequipol- 
lence ; all, in fact, would be so were it not that ordinary 
speech loses somewhat in the process, owing to the 
indefiniteness of the syllogistic symbol for particular 
quality. Some. And in truth all such transmutations 
of expression are as much entitled to the dignity of 
being called Immediate Inferences as most of the 
processes so entitled. 

Dr. Bain uses the word with an approach to this 
width of application in discussing all that is now most 
commonly called Immediate Inference under the title 
of Equivalent Forms. The chief objection to this 
usage is that the Converse per accidens is not strictly 
equivalent. A debater may want for his argument less 
than the strict equivalent, and content himself with 
educing this much from his opponent's admission. 
(Whether Dr. Bain is right in treating the Minor and 
Conclusion of a Hypothetical Syllogism as being 
equivalent to the Major, is not so much a question of 
naming.) 

But in the history of the subject, the traditional 
usage has been to confine iEquipollence to cases of 
equivalence between positive and negative forms of 
expression. ** Not all are," is equivalent to " Some 
are not " : " Not none is," to ** Some are ". In Pre- 
Aldrichian text-books, i3£quipollence corresponds 



The Implication ef Propositions. 149 

mainly to what it is now customary to call {e.g.. 
Fowler, pt. iii. c. ii., Keynes, pt. ii. c. vii.) Immediate 
Inference based on Opposition. The denial of any 
proposition involves the admission of its contradictory. 
Thus, if the negative particle " Not" is placed before 
the sign of Quantity, All or Some, in a proposition, 
the resulting proposition is equivalent to the Contra- 
dictory of the original. Not all S is P = Some 8 is 
not P. Not any S is P = No S is P. The mediaeval 
logicians tabulated these equivalents, and also the 
forms resulting from placing the negative particle 
after, or both before and after, the sign of Quantity. 
Under the title of iEquipollence, in fact, they con- 
sidered the interpretation of the negative particle 
generally. If the negative is placed after the universal 
sign, it results in the Contrary : if both before and 
after, in the Subaltern. The statement of these 
equivalents is a puzzling exercise which no doubt 
accounts for the prominence given it by Aristotle and 
the Schoolmen. The latter helped the student with 
the following Mnemonic line: Pr(z Contradic, post 
Contrar,j prcB postque Subaltern} 

^ There can be no doubt that in their doctrine of -^quipcllcnts, 
the Schoolmen were trying to make plain a real difficulty in inter- 
pretation, the interpretation of the force of negatives. Their results 
would have been more obviously useful if they had seen their way 
to generalising them. Perhaps too they wasted their strength in 
applying it to the artificial syllogistic forms, which men do not 
ordinarily encounter except in the manipulation of syllogisms. 
Their results might have been generalised as follows : — 

(i) A " not " placed before the sign of Quantity contradicts the 
whole proposition. Not "All S is P," not •*No S is P," not 
" Some S is P," not " Some S is not P," are equivalent respec- 
tively to contradictories of the propositions thus negatived. 

(a) A " not " placed after the sign of Quantity affects the 



15© The Interpretation of Propositions. 

To iEquipollence belonged also the manipulation 
of the forms known after the Sum^nulce as Exponibiles, 
notably Exclusive and Exceptive propositions^ such as 
None but barristers are eligible, The virtuous alone 
are happy. The introduction of a negative particle 
into these already negative forms makes a very trying 
problem in interpretation. The aequipollence of the 
Exponibiles was dropped from text-books long before 
Aldrich, and it is the custom to laugh at them as 
extreme examples of frivolous scholastic subtlety : but 
most modern text-books deal with part of the doctrine 
of the Exponibiles in casual exercises. 

Curiously enough, a form left unnamed by the 
scholastic logicians because too simple and useless, 
has the name Equipollent appropriated to it, and to 
it alone, by Ueberweg, and has been adopted under 
various names into all recent treatises. 

Bain calls it the Formal Obverse,^ and the title of 

copula, and amounts to inverting its Quality, thus denying the 
predicate term of the same quantity of the subject term of which 
it was originally affirmed, and vice versd. 

All S is " not " P = No S is P. 
No S is "not'* P = All Sis P. 
Some S is " not " P = Some S is not P. 
Some S is " not " not P = Some S is P. 
(3) If a " not " is placed before as well as after, the resulting 
forms are obviously equivalent (under Rule i) to the assertion of 
the contradictories of the forms on the right (in the illustration of 
Rule 2). 



Not 
Not 
Not 
Not 



All Sis "not" P :^NoSi8P 

No Sis "not" P ^tAUSisP 
Some S is " not " P ^ Some Sis not P 
Some S is " not '» not P = Some S is P 



ac Some S is P. 
= Some S is not P. 
=: All S is P. 
3C No S is P. 



^ Formal to distinguish it from what he called the MaUrial 
ObvefsCf about which more presently. 



Ttie tmptication of Propositions, i^i 

Obversion (which has the advantage of rhyming with 
Conversion) has been adopted by Keynes, Miss 
Johnson, and others. 

Fowler (following Karslake) calls it Permutation. 
The title is not a happy one, having neither rhyme 
nor reason in its favour, but it is also extensively used. 

This immediate inference is a very simple affair to 
have been honoured with such a choice of terminology. 
" This road is long : therefore, it is not short," is an 
easy inference : the second proposition is the Obverse, 
or Permutation, or Equipollent, or (in Jevons's title) 
the Immediate Inference by Privative Conception, of 
the first. 

The inference, such as it is, depends on the Law of 
Excluded Middle. Either a term P, or its contradic- 
tory, not-P, must be true of any given subject, S : 
hence to affirm P of all or some S, is equivalent to 
denying not-P of the same : and, similarly, to deny P, 
is to affirm not-P. Hence the rule of Obversion ; 
— Substitute for the predicate term its Contrapositive, * 
and change the Quality of the proposition. 

All S is P = No S is not-P, 
No S is P = All S is not-P. 
Some S is P « Some S is not not-P. 
Some S is not P = Some S is not-P. 

Conversion. 

The process takes its name from the interchange of 
the terms. The Predicate-term becomes the Subject- 
term, and the Subject-term the Predicate-term. 

When propositions are analysed into relations of 

^ The mediaeval word for the opposite of a term, the word 
Contradictory being confined to the propositional form. 



t^i The Interpretation of Propositions, 

inclusion or exclusion between terms, the assertion 
of any such relation between one term and another, 
implies a Converse relation between the second term 
and the first. The statement of this implied assertion 
is technically known as the Converse of the original 
proposition, which may be called the Convertend. 

Three modes of Conversion are commonly recog- 
nised : — {a) Simple Gonversion ; {b) Conyersion per 
accidens or by limitation ; if) ConYersion by Contra- 
position. 

(a) E and I can be simply converted, only the terms 
being interchanged, and Quantity and Quality remain- 
ing the same. 

If S is wholly excluded from P, P must be wholly 
excluded from S. If Some S is contained in P, then 
Some P must be contained in S. 

(b) A cannot be simply converted. To know that 
All S is contained in P, gives you no information 
about that portion of P which is outside S. It only 
enables you to assert that Some P is S ; that portion 
of P, namely, which coincides with S. 

O cannot be converted either simply or per accidens. 
Some S is not P does not enable you to make any 
converse assertion about P. All P may be S, or No 
P may be S, or Some P may be not S. All the three 
following diagrams are compatible with Some S being 
excluded from P. 




0© (s® 



[c) Another mode of Conversion, known by mediaeval 
logicians following Boethius as Conversio per contra- 



The Implication of Propositions . 153 

positionem terminoruniy is useful in some syllogistic 
manipulations. This Converse is obtained by substi- 
tuting for the predicate term its Contrapositive or 
Contradictory, not-P, making the consequent change 
of Quality, and simply converting. Thus All S is P 
is converted into the equivalent No not-P is S.* 

Some have called it " Conversion by Negation," but 
"negation" is manifestly too wide and common a 
word to be thus arbitrarily restricted to the process of 
substituting for one term its opposite. 

Others (and this has some mediaeval usage in its 
favour, though not the most intelligent) would call 
the form All not-P is not-S (the Obverse or Permu- 
tation of No not-P is S), the Converse by Contra- 
position. This is to conform to an imaginary rule 
that in Conversion the Converse must be of the same 
Quality with the Convertend. But the essence of 
Conversion is the interchange of Subject and Predicate : 
the Quality is not in the definition except by a bungle : 
it is an accident. No not-P is S, and Some not-P is 
S are the forms used in Syllogism, and therefore 
specially named. Unless a form had a use, it 
was left unnamed, like the Subalternate forms of 
Syllogism : Nomen habent nullum : nee, si bene 
coUigis, usum. 



1 It IS to be regretted that a practice has recently crept in of 
calling this form, for shortness, the Contrapositive simply. By 
long-established usage, dating from Boethius, the word Contra- 
positive is a technical name for a terminal form, not-A, and it is 
still wanted for this use. There is no reason why the proposi- 
tional form should not be called the Converse by Contraposition, 
or the Contrapositive Converse, in accordance with traditional 
usage. 



154 The Interpretation of Propositions. 

Table of Contrapositive Converses. 

Con. Con. 
All SisP No not- Pis S 

No S is P Some not-P is S 

Some S is not P Some not-P is S 

Some S is P None. 

When not-P is substituted for P, Some S is P 
becomes Some S is not not-P, and this form is 
inconvertible. 

Other Forms of Immediate Inference. 

I have already spoken of the Immediate Inferences 
based on the rules of Contradictory and Contrary 
Opposition (see p. 145). 

Another process was observed by Thomson, and 
named Immediate Inference by Added Determinants^ 
If it is granted that " A negro is a fellow-creature," 
it follows that ** A negro in suffering is a fellow- 
creature in suffering ". But that this does not follow 
for every attribute* is manifest if you take another 
case : — " A tortoise is an animal : therefore, a fast 
tCHloise is a fast animal" The form, indeed, holds 
in cases not worth specifying : and is a mere handle 
for quibbling. It could not be erected into a general 
rule unless it were true that whatever distinguishes a 
species within a class, will equally distinguish it in 
every class in which the first is included. 

Modal Consequence has also been named among 
the forms of Immediate Inference. By this is meant 
the inference of the lower degrees of certainty from the 

^ Cf. Stock, part iii. c. vii. ; Bain, Deduction^ p. log. 



The Implication of Propositions. 155 

higher. Thus must be is said to imply may be; and 
None can be to imply None is. 

Dr. Bain includes also Material Obversion^ the 
analogue of Formal Obversion applied to a Subject. 
Thus Peace is beneficial to commerce, implies that 
War is injurious to commerce. Dr. Bain calls this 
Material Obversion because it cannot be practised 
safely without reference to the matter of the proposition. 
We shall recur to the subject in another chapter. 



Chapter !¥• 
THE COUNTER-IMPLICATION OF PftpPOSITIONS. 

In discussing the Axioms of Dialectic, Hndicated that 
the propositions of common speech have a certain 
negative implication, though this does not depend 
upon any of the so-called Laws of Thought, Identity, 
Contradiction, and Excluded Middle. Since, however, 
the counter-implicate is an important guide in the 
interpretation of propositions, it is desirable to recog- 
nise it among the modes of Immediate Inference. 

I propose, then, first, to show that people do 
ordinarily infer at once to a counter-sense ; second, to 
explain briefly the Law of Thought on which such an 
inference is justified ; and, third, how this law may be 
applied in the interpretation of propositions, with a 
view to making subject and predicate more definite. 

Every affirmation about anything is an implicit 
negation about something else. Every say is a gain- 
say. That people ordinarily act upon this as a rule of 
interpretation a little observation is sufficient to show : 
and we find also that those who object to having their 
utterances interpreted by this rule often shelter them- 
selves under the name of Logic. 

Suppose, for example, that a friend remarks, when 
the conversation turns on children, that John is a good 
boy, the natural inference is that the speaker has in his 

(156) 



The Counter-Implication of Propositions, 157 

mind another child who is not a good boy. Such an 
inference would at once be drawn by any actual hearer, 
and the speaker would protest in vain that he said 
nothing about anybody but John. Suppose there are 
two candidates for a school appointment, A and B, 
and that stress is laid upon the fact that A is an 
excellent teacher. A's advocate would at once be 
understood to mean that B was not equally excellent 
as a teacher. 

The fairness of such inferences is generally recog- 
nised. A reviewer, for example, of one of Mrs. 
Oliphant's historical works, after pointing out some 
small errors, went on to say that to confine himself to 
censure of small points, was to acknowledge by impli- 
cation that there were no important points to find 
fault with. 

Yet such negative implications are often repudiated 
as illogical. It would be more accurate to call them 
extra-logical. They are not condemned by any logical 
doctrine : they are simply ignored. They are extra- 
logical only because they are not legitimated by the 
Laws of Identity, Contradiction, and Excluded Middle: 
and the reason why Logic confines itself to those laws 
is that they are sufficient for Syllogism and its subsidiary 
processes. 

But, though extra-logical, to infer a counter-implicate 
is not unreasonable : indeed, if Definition, clear vision \ 
of things in their exact relations, is our goal rather 
than Syllogism, a knowledge of the counter-implicate 
is of the utmost consequence. Such an implicate 
there must always be under an all-pervading Law of 
Thought which has not yet been named, but which 
may be called tentatively the law of Homogeneous 
Counter-relativity. The title, one hopes, is sufficiently 



15^ JJfe Interpretation of Propositions. 

technical-looking : though cumbrous, it is descriptive. 
The law itself is simple, and may be thus stated and 
explained. 



The Law of Homogeneous Counter-relativity. 

Every positive in thought has a contrapositive, 
and the positive and contrapositive are of the 
same kind. 

The first clause of our law corresponds with Dr. 
Bain's law of Discrimination or Relativity : it is, 
indeed, an expansion and completion of that law. 
Nothing is known absolutely or in isolation ; the 
various items of our knowledge are inter-relative; 
everything is known by distinction from other things. 
Light is known as the opposite of darkness, poverty of 
riches, freedom of slavery, in of out ; each shade of 
colour by contrast to other shades. What Dr. Bain 
lays stress upon is the element of difference in this 
inter-relativity. He bases this law of our knowledge 
on the fundamental law of our sensibility that change 
of impression is necessary to consciousness. A long 
continuance of any unvaried impression results in 
insensibility to it. We have seen instances of this in 
illustrating the maxim that custom blunts sensibility 
(p. 74). Poets have been beforehand with philosophers 
in formulating this principle. It is expressed with the 
greatest precision by Barbour in his poem of " The 
Bruce," where he insists that men who have never 
known slavery do not know what freedom is. 

Thus contrar thingis evermare 
Discoverings of t' other are. 



The Counier-Implkaiton of Propositions. 159 

Since, then, everything that comes within our con- 
sciousness comes as a change or transition from 
something else, it results that our knowledge is counter- 
relative. It is in the clash or conflict of impressions 
that knowledge emerges : every item of knowledge has 
its illuminating foil, by which it is revealed, over against 
which it is defined. Every positive in thought has its 
contrapositive. 

So much for the element of difference. But this is 
not the whole of the inter-relativity. The Hegelians 
rightly lay stress on the common likeness that connects 
the opposed items of knowledge. 

** Thought is not only distinction ; it is, at the same time, 
relation^ If it marks off one thing from another, it, at the 
same time, connects one thing with another. Nor can either of 
these functions of thought be separated from the other : as 
Aristotle himself said, the knowledge of opposites is one. A 
thing which has nothing to distinguish it is unthinkable, but 
equally unthinkable is a thing which is so separated from all 
other things as to have no community with them. If then the 

1 It is significant of the unsuitableness of the vague unqualified 
word Relativity to express a logical distinction that Dr. Bain calls 
his law the Law of Relativity simply, having regard to the relation 
of difference, i,e,^ to Counter- Relativity, while Dr. Caird applies 
the name Relativity simply to the relation of likeness, i.^., to Co- 
relativity. It is with a view to taking both forms of relation 
into account that I name our law the Law of Homogeneous 
Counter-relativity. The Protagorean Law of Relativity has 
regard to yet another relation, the relation of knowledge 
to the knowing mind: these other logical laws are of relations 
among the various items of knowledge. Aristotle's category of 
Relation is a fourth kind of relation not to be confused with the 
others. ** Father — son,*' " uncle — nephew,** " slave — master," are 
relata in Aristotle's sense : " father,** " uncle '* are homogeneous 
counter-relatives, varieties of kinship ; so " slave,** " freeman *' are 
counter -relatives in social status. 



i6o The Interpntaiion of Propositions. 

law of contradiction be taken as asserting the self-identity of 
things or thoughts in a sense that excludes their community — in 
other words, if it be not taken as limited by another law which 
asserts the relativity of the things or thoughts distinguished — it 
involves a false abstraction. ... If, then, the world, as an intelli- 
gible world, is a world of distinction, differentiation, individuality, 
it is equally true that in it as an intelligible world there are no 
absolute separations or oppositions, no antagonisms which cannot 
be reconciled." ^ 

In the penultimate sentence of this quotation Dr. 
Caird differentiates his theory against a Logical counter- 
theory of the Law of Identity, and in the last sentence 
against an Ethical counter-theory : but the point here 
is that he insists on the relation of likeness among 
opposites. Every impression felt is felt as a change 
or transition from something else : but it is a variation 
of the same impression — the something else, the 
contrapositive, is not entirely different. Change 
itself is felt as the opposite of sameness, difference 
of likeness, and likeness of difference. We do not 
differentiate our impression against the whole world, 
as it were, but against something nearly akin to it — 
upon some common ground. The positive and the 
contrapositive are of the same kind. 

Let us surprise ourselves in the act of thinking and 
we shall find that our thoughts obey this law. We 
take note, say, of the colour of the book before us : 
we differentiate it against some other colour actually 
before us in our field of vision or imagined in our 
minds. Let us think of the blackboard as black : the 
blackness is defined against the whiteness of the 
figures chalked or chalkable upon it, or against the 
colour of the adjacent wall. Let us think of a man as 

^ Dr. Caird's Hegel^ p. 134. 



The Counter-Implication of Propositions, i6i 

a soldier ; the opposite in our minds is not the colour 
of his hair, or his height, or his birthplace, or his 
nationality, but some other profession — soldier, sailor, 
tinker, tailor. It is always by means of some contra- 
positive that we make the object of our thoughts 
definite ; it is not necessarily always the same opposite, 
but against whatever opposite it is, they are always 
homogeneous. One colour is contradistinguished 
from another colour, one shade from another shade : 
colour may be contradistinguished from shape, but it 
is within the common genus of sensible qualities. 

A curious confirmation of this law of our thinking 
has been pointed out by Mr. Carl Abel.* In Egyptian 
hieroglyphics, the oldest extant language, we find, he 
says, a large number of symbols with two meanings, 
the one the exact opposite of the other. Thus the 
same symbol represents strong 2Sidi weak; above — below ; 
with — without ; for — against. This is what the Hege- 
lians mean by the reconciliation of antagonisms in 
higher unities. They do not mean that black is white, 
but only that black and white have something in 
common — they are both colours. 

I have said that this law of Homogeneous Counter- 
relativity has not been recognised by logicians. This, 
however, is only to say that it has not been explicitly 
formulated and named, as not being required for 
Syllogism; a law so all-pervading could not escape 
recognition, tacit or express. And accordingly we 
find that it is practically assumed in Definition : it is 
really the basis of definition per genus et differentiam. 
When we wish to have a definite conception of 
anything, to apprehend what it is, we place it in some 

^ See article on Counter- Sense, Contemporary Review^ April, 
X884. 



i62 The Interpretations of Propositions. 

genus and distinguish it from species of the same. In 
fact our law might be called the Law of Specification : 
in obeying the logical law of what we ought to do with 
a view to clear thinking, we are only doing with 
exactness and conscious method what we all do and 
cannot help doing with more or less definiteness in our 
ordinary thinking. 

It is thus seen that logicians conform to this law 
when they are not occupied with the narrow considera- 
tions proper to Syllogism. And another unconscious 
recognition of it maybe found in most logical text-books. 
Theoretically the not-A of the Law of Contradiction- 
(A is not not-A)— is an infinite term. It stands for 
everything but A. This is all that needs to be assumed 
for Conversion and Syllogism. But take the examples 
given of the Formal Obverse or Permutation, " All mei^ 
are fallible". Most authorities would give as thd 
Formal Obverse of this, " No men are infallible "; 
But, strictly speaking, " infallible " is of more limited) 
and definite signification than not-fallible. Not-fallible,! 
other than fallible, is brown, black, chair, table, andj 
every other nameable thing except fallible. Thus inj 
Obversion and Conversion by Contraposition, the! 
homogeneity of the negative term is tacitly assumed; 
it is assumed that A and not-A are of the same kind. 

Now to apply this Law of our Thought to the inter- 
pretation of propositions. Whenever a proposition is 
uttered we are entitled to infer at once (or immediately) 
that the speaker has in his mind some counter-proposi- 
tion, in which what is overtly asserted of the ostensible 
subject is covertly denied of another subject. And we 
must know what this counter-proposition, the counter- 
implicate is, before we can fully and clearly understand 



The Counter- Implication of Propositions. 163 

his meaning. But inasmuch as any positive may have 
more than one contrapositive, we cannot tell immedi- 
ately or without some knowledge of the circumstances 
or context, what the precise counter-implicate is. The 
peculiar fallacy incident to this mode of interpretation 
is, knowing that there must be some counter-implicate, 
to jump rashly or unwarily to the conclusion that it is 
some definite one. 

Dr. Bain applies the term Material Obverse to the 
form, Not-S is not P, as distinguished from the form 
S is not not-P, which he calls the Formal Obverse, on 
the ground that we can infer the Predicate-contrapositive 
at once from the form, whereas we cannot tell the 
Subject-contrapositive without an examination of the 
matter. But in truth we cannot tell either Predicate- 
contrapositive or Subject-contrapositive as it is in the 
mind of the speaker from the bare utterance. We can 
only tell that if he has in his mind a proposition 
definitely analysed into subject and predicate, he must 
have contrapositives in his mind of both, and that they 
must be homogeneous. Let a man say, " This book 
is a quarto". For all that we know he may mean 
that it is not a folio or that it is not an octavo : we 
only know for certain, under the law of Homogeneous 
Counter-relativity, that he means some definite other 
size. Under the same law, we know that he has a 
homogeneous contrapositive of the subject, a subject 
that admits of the same predicate, some other book 
in short. What the particular book is we do not 
know. 

It would however be a waste of ingenuity to dwell 
upon the manipulation of formulae founded on this law. 
The practical concern is to know that for the interpre- 
tation of a proposition, a knowledge of the counter- 



1 64 The Jnterpretation of Propositions, 

implicate, a knowledge of what it is meant to deny, is 
essential. 

The manipulation of formulae, indeed, has its own 
special snare. We are apt to look for the counterparts 
of them in the grammatical forms of common speech. 
Thus, it might seem to be a fair application of our law 
to infer from the sentence, ** Wheat is dear," that the 
speaker had in his mind that Oats or Sugar or Shirting 
or some other commodity is cheap. But this would be 
a rash conclusion. The speaker may mean this, but 
he may also mean that wheat is dear now as compared 
with some other time : that is, the Positive subject in 
his mind may be " Wheat as now," and the Contra- 
positive " Wheat as then ". So a man may say, "All 
men are mortal," meaning that the angels never taste 
death, " angels " being the contrapositive of his subject 
" men ". Or he may mean merely that mortality is a 
sad thing, his positive subject being men as they are, 
and his contrapositive men as he desires them to be. 
Or his emphasis may be upon the a//, and he may 
mean only to deny that some one man in his mind 
(Mr. Gladstone, for example) is immortal. It would 
be misleading, therefore, to prescribe propositions as 
exercises in Material Obversion, if we give that name 
to the explicit expression of the Contrapositive Subject : 
it is only from the context that we can tell what this 
is. The man who wishes to be clearly understood 
gives us this information, as when the epigrammatist 
said : " We are all fallible — even the youngest of us ". 

But the chief practical value of the law is as a guide 
in studying the development of opinions. Every 
doctrine ever put forward has been put forward in 
opposition to a previous doctrine on the same subject. 
Until we know what the opposed doctrine is, we cannot 



The Counter- Implication of Propositions. 165 

be certain of the meaning. We cannot gather it with 
precision from a mere study of the grammatical or 
even (in the narrow sense of the word) the logical con- 
tent of the words used. This is because the framers 
of doctrines have not always been careful to put them 
in a clear form of subject and predicate, while their 
impugners have not moulded their denial exactly on 
the language of the original. No doubt it would have 
been more conducive to clearness if they had done so. 
But they have not, and we must take them as they 
are. Thus we have seen that the Hegelian doctrine of 
Relativity is directed against certain other doctrines in 
Logic and in Ethics ; that Ultra-^Nominalism is a con- 
tradiction of a certain form of Ultra-Realism ; and that 
various theories of Predication each has a backward 
look at some predecessor. 

I quote from Mr. A. B. Walkley a vtty happy appli- 
cation of this principle of interpretation :-— 

** It has always been a matter for speculation why so sagacious 
an observer as Diderot should have formulated the wild paradox 
that the greatest actor is he who feels his part the least. Mr. 
Archer's bibliographical research has solved this riddle. Diderot's 
paradox was a protest against a still wilder one. It seems that a 
previous eighteenth century writer on the stage, a certain Saint- 
Albine, had advanced the fantastic propositions that none but a 
magnanimous man can act magnanimity, that only lovers can 
do justice to a love scene, and kindred assertions that read like 
variations on the familiar * Who drives fat oxen must himself be 
fat '. Diderot saw the absurdity of this ; he saw also the essentially 
artificial nature of the French tragedy and comedy of his own day; 
and he hastily took up the position which Mr. Archer has now 
shown to be untenable." 

This instance illustrates another principle that has 
to be borne in mind in the interpretation of doctrines 
from their historical context of counter-implication. 



1 66 The Interpretation of Propositions, 

This is the tendency that men have to put doctrines in 
too universal a form, and to oppose universal to uni- 
versal, that is, to deny with the flat contrary, the very 
reverse, when the more humble contradictory is all 
that the truth admits of. If a name is wanted for this 
tendency, it might be called the tendency to Over- 
Contradiction. Between ** All are" and "None are," 
the sober truth often is that " Some are '* and " Some 
are not," and the process of evolution has often con- 
sisted in the substitution of these sober forms for their 
more vioieet prede^essQi'S" 



PART IV. 

THE INTERDEPENDENCE OF PROPOSI- 
TIONS.— MEDIATE INFERENCE.— 
SYLLOGISM, 



Chapter L 
THE SYLLOGISM. 



We have already defined mediate inference as the 
derivation of a conclusion from more than one propo- 
sition. The type or form of a mediate inference fully 
expressed consists of three propositions so related that 
one of them is involved or implied in the other two. 

Distraction is exhausting. 
Modern life is full of distraction. 
.•. Modern life is exhausting. 

We say nothing of the truth of these propositions. 
I purposely choose questionable ones. But do they 
hang together ? If you admit the first two, are you 
bound in consistency to admit the third ? Is the 
r truth of the conclusion a necessary consequence of 
' the truth of the premisses ? If so^ it is a valid 
mediate inference from them. 

(167) 



1 68 The Interdependence of Propositions, 

When one of the two premisses is more general than 
the conclusion, the argument is said to be Deducti¥e. 
You lead down from the more general to the less 
general. The general proposition is called the Major 
Premiss, or Grounding Proposition, or Sumption : the 
other premiss the Minor, or Applying Proposition, or 
Subsumption. 

Undue haste makes waste. 
This is a case of undue hasting, 
••• It is a case of undue wasting. 

We may, and constantly do, apply principles and 
draw conclusions in this way without making any 
formal analysis of the propositions. Indeed we reason 
mediately and deductively whenever we make any 
application of previous knowledge, although the 
process is not expressed in propositions at all and is 
performed so rapidly that we are not conscious of the 
steps. 

For example, I enter a room, see a book, open it 
and begin to read. I want to make a note of some- 
thing : I look round, see a paper case, open it, take a 
sheet of paper and a pen, dip the pen in the ink and 
proceed to write. In the course of all this, I act upon 
certain inferences which might be drawn out in the 
form of Syllogisms. First, in virtue of previous 
knowledge I recognise what lies before me as a book. 
The process by which I reach the conclusion, though 
it passes in a flash, might be analysed and expressed 
in propositions. 

Whatever presents certain outward appearances, 

contains readable print. 
This presents such appearancein 
V It contains readable print. 



The Syllogism. 169 

So with the paper case, and the pen, and the ink. I 
infer from peculiar appearances that what I see contains 
paper, that the liquid will make a black mark on the 
white sheet, and so forth. 

We are constantly in daily life subsuming particulars 
under known universals in this way. " Whatever has 
certain visible properties, has certain other properties : 
this has the visible ones : therefore, it has the others " 
is a form of reasoning constantly latent in our minds. 

The Syllogism may be regarded as the explicit 
expression of this type of deductive reasoning ; that is, 
as the analysis and formal expression of this cvery-day 
process of applying known universals to particular 
cases. Thus viewed it is simply the analysis of a 
mental process, as a psychological fact ; the analysis 
of the procedure of all men when they reason from 
$igns ; the analysis of the kind of assumptions they 
make when they apply knowledge to particular cases. 
The assumptions may be warranted, or they may not: 
but as a matter of fact the individual who makes the 
confident inference has such assumptions and sub- 
sumptions latent in his mind* 

But practically viewed, that is logically viewed, if 
you regard Logic as a practical science, the Syllogism 
is a contrivance to assist the correct performance of 
reasoning together or syllogising in difficult cases. It 
applies not to mental processes but to results of such 
expressed in words, that is, to propositions. Where 
the Syllogism comes in as a useful form is when 
certain propositions are delivered to you ab extra as 
containing a certain conclusion ; and the connexion is 
not apparent. These propositions are analysed and 
thrown into a form in which it is at once apparent 
whether the alleged connexion exists. This form is 



17© The Interdependence of Propositions, 

the Syllogism : it is, in effect, an analysis of given 
arguments. 

It was as a practical engine or organon that it was 
invented by Aristotle, an organon for the syllogising of 
admissions in Dialectic. The germ of the invention 
was the analysis of propositions into terms. The 
syllogism was conceived by Aristotle as a reasoning 
together of terms. His prime discovery was that 
whenever two propositions necessarily contain or imply 
a conclusion, they have a common term, that is, only 
three terms between them : that the other two terms 
which differ in each are the terms of the conclusion ; 
and that the relation asserted in the conclusion between 
its two terms is a necessary consequence of their 
relations with the third term as declared in the 
premisses. 

Such was Aristotle's conception of the Syllogism 
and such it has remained in Logic. It is still, strictly 
speaking, a syllogism of terms : of propositions only 
secondarily and after they have been analysed. The 
conclusion is conceived analytically as a relation 
between two terms. In how many ways may this 
relation be established through a third term? The 
various moods and figures of the Syllogism give the 
answer to that question. 

The use of the very abstract word ** relation " makes 
the problem appear much more difficult than it really 
is. The great charm of Aristotle's Syllogism is its 
simplicity. The assertion of the conclusion is reduced 
to its simplest possible kind, a relation of inclusion or 
exclusion, contained or not contained. To show that 
the one term is or is not contained in the other we 
have only to find a third which contains the one and is 
contained or not contained in the other. 



fhe Syllogism, 171 

The practical difficulties, of course, consist in the 
reduction of the conclusions and arguments of common 
speech to definite terms thus simply related. Once 
they are so reduced, their independence or the 
opposite is obvious. Therein lies the virtue of the 
Syllogism. 

Before proceeding to show in how many ways two 
terms may be Syllogised through a third, we must have 
technical names for the elements. 

The third term is called the Middl© (M) (to puitrov) : 
the other two the Extremes (a/cpa). 

The Extremes are the Subject (S) and the Predicate 
(P) of the conclusion. 

In an affirmative proposition (the normal fonn) S 
is contained in P: hence P is called the Major ^ term 
(to /Aci^ov), and S the Minor (to cXarrov), being respec- 
tively larger and smaller in extension. All difficulty 
about the names disappears if we remember that in 
bestowing them we start from the conclusion. That 
was the problem (TrpopXrj/ia) or thesis in dialectic, the 
question in dispute. 

The two Premisses, or propositions giving the 
relations between the two Extremes and the Middle, 
are named on an equally simple ground. 

One of them gives the relation between the 
Minor Term, S, and the Middle, M. S, All or Some, 
is or is not in M. This is called the Minor 
Premiss. 

The other gives the relation between the Major 



^ Aristotle calls the Major the First {rh irpSrov) and the Minor 
the Last (t^ ^cxaroy), probably because that was their order in the 
conclusion when stated in his most usual form, •• P is predicated 
^ %/' ®r " P belongs to B •% 



172 The Interdependence of Propositions. 

Term and the Middle. M, All or Some, is or is not in 
P. This is called the Major Premiss.* 

^When we speak of the Minor or the Major simply, the 
reference is to the terms. To avoid a confusion into which 
beginners are apt to stumble, and at the same time to emphasise 
the origin of the names, the Premisses might be spoken of at first 
as the Minor's Premiss and the Major's Premiss. It was only in 
the Middle Ages when the origin of the Syllogism had been for- 
gotten, that the idea arose that the terms were called Major and 
Minor because they occurf@d la the MajoE and the Minor 
Premiss respectively^ 



Chapter IL 

FIGURES AND MOODS OF THE SYLLOGISM. 

L — ^The First Figure. 

The forms (technically called Moods, i>., modes) of 
the First Figure are founded on the simplest relations 
with the Middle that will yield or that necessarily 
involve the disputed relation between the Extremes. 

The simplest type is stated by Aristotle as follows : 
" When three terms are so related that the last (the 
Minor) is wholly in the Middle, and the Middle wholly 
either in or not in the first (the Major) there must be 
a perfect syllogism of the Extremes ". ^ 

When the Minor is partly in the Middle, the 
Syllogism holds equally good. Thus there are four 
possible ways in which two terms (opot, plane enclo- 
sures) may be connected or disconnected through a 
third. They are usually represented by circles as 
being the neatest of figures, but any enclosing outline 
answers the purpose, and the rougher and more 
irregular it is the more truly will it represent the 
extension of a word. 



^ "Orav oZv Bpoi rpcTs o$to>5 ^xaxrt wphs aWiiKovs Sxm rhv ttrxourov 
iv 3Ay fTvoi ry iuL€(r(pj Koi rhv jnctrov 4y Z\cp rep irpcory fj clvai ^ /i^ 
€hpUi kvdyiai rwv ^Kpwp clvai (rvWoyifffjiby T€\€Loy. (Anal. Prior., i. 4.) 

(^73) 



IV4 



The Interdependence of Propositions. 



Conclusion A. 
All M is in P. 
All S is in M. 
All S is ia F. 

Conclusion E. 
No M is in P. 
All S is in M« 
No S is in R 

Conclusion L 
All M is in P. 
Some S is in M. 
Some S is in P. 



Conclusion O. 
No M is in P, 
Some S is in M. 
Some S is not in P. 




These four forms constitute what are known as the 
moods of the First Figure of the Syllogism, Seeing 
that all propositions may be reduced to one or other 
of the four forms, A, E, I, or O, we have in these 
premisses abstract types of every possible valid argu- 
ment from general principles. It is all the same 
whatever be the matter of the proposition. Whether 
the subject of debate is mathematical, physical, social, 
or political, once premisses in these forms are con- 
ceded, the conclusion follows irresistibly, ex vi formce, 
ix necessitate formm. If an argument can be analysed 



Figures and Moods of the Syllogism, 175 

into these forms, and you admit its propositions, you 
are bound in consistency to admit the conclusion — 
unless you are prepared to deny that if one thing is in 
another and that other in a third, the first is in the 
third, or if one thing is in another and that other 
wholly outside a third, the first is also outside the 
third. 

This is called the Axiom of Syllogismi. The most 
common form of it in Logic is that known as the 
Dictum^ or Regula de Omni et Nullo : " Whatever is 
predicated of All or None of a term, is predicated of 
whatever is contained in that term'\ It has been 
expressed with many little variations, and there has 
been a good deal of discussion as to the best way of 
expressing it, the relativity of the word best being often 
left out of sight. Best for what purpose ? Practically 
that form is the best which best commands general 
assent, and for this purpose there is little to choose 
between various ways of expressing it. To make it 
easy and obvious it is perhaps best to have two 
separate forms, one for affirmative conclusions and 
one for negative. Thus : " Whatever is affirmed of 
all M, is affirmed of whatever is contained in M : and 
whatever is denied of all M, is denied of whatever is 
contained in M ". The only advantage of including 
the two forms in one expression, is compendious 
neatness. " A part of a part is a part of the whole," is 
a neat form, it being understood that an individual or 
a species is part of a genus. "What is said of a 
whole, is said of every one of its parts," is really a 
sufficient statement of the principle : the whole being 
the Middle Term, and the Minor being a part of it, 
the Major is predicable of the Minor affirmatively or 
negatively if it is predicable similarly of the Middle. 



176 The Interdependence of Propositions. 

This Axiom, as the name imports, is indemonstrable. 
As Aristotle pointed out in the case of the Axiom of 
Contradiction, it can be vindicated, if challenged, only 
by reducing the challenger to a practical absurdity. 
You can no more deny it than you can deny that if a 
leaf is in a book and the book is in your pocket, the 
leaf is in your pocket. If you say that you have a 
sovereign in your purse and your purse is in your 
pocket, and yet that the sovereign is not in your 
pocket : will you give me what is in your pocket for 
the value of the purse ? 



II. — The Minor Figures of the Syllogism, and 
THEIR Reduction to the First. 

The word Figure (o7(^/xa) applies to the form oi 
figure of the premisses, that is, the order of the terms 
in the statement of the premisses, when the Major 
Premiss is put first, and the Minor second. 

In the First Figure the order is 

M P 
S M. 

But there are three other possible orders or figures, 
namely :— 



Fig. ii. 


Fig. Hi. 


Fig. IT. 


PM 


MP 


PM 


SM 


MS 


MS. 



It results from the doctrines of Conversion that 
valid arguments may be stated in these forms, 
inasmuch as a proposition in one order of terms may 
be equivalent to a proposition in another. Thus No 



Figures ana Moods of the Syllogism. 177 

M IS in P IS convertible with No P is in M : con 
sequently the argument 

No P is in M 

All S is in M, 

in the Second Figure is as much valid as when it is 

stated in the First- 
No M is in P 
All S is in M. 

Similarly, since All M is in S is convertible into Some 
S is in M, the following arguments are equally 
valid :~ 

Fig. Hi, Fig. i. 

All M is in P All M is in P 

All M is in S ^ Some S is in M. 

Using both the above Converses in place of theii 

Convertends, we have- 
Fig, iv. Fig. i. 
No P is in M No M is in P 
All M is in S ~ Some S is in M. 

It can be demonstrated (we shall see presently how) 
that altogether there are possible four valid forms or 
moods of the Second Figure, six of the Third, and five 
of the Fourth. An ingenious Mnemonic of these 
various moods and their reduction to the First Figure 
by the transposition of terms and premisses has come 
down from the thirteenth century. The first line names 
the moods of the First, Normal, or Standard Figure. 



178 The Interdependence of Propositions. 

BKrbArk, CElArEnt, DArll, FErlO^ue prions; 
CEsArE, CAmEstrEs, FEstInO, BArO^O, secundge ; 
Tertia DArAptl, DlsAmls, DAtlsI, FEiAptOn, 
BOkArdOj FErlsO^ue, habet ; quarta insuper addit, 
BrAmAntlP, CAmEnEs, DImArls, FEsApO, FrEsIsOn. 

The vowels in the names of the Moods indicate the 
propositions jf the Syllogism in the four forms, 
A E I O. To write out any Mood at length you have 
only to remember the Figure, and transcribe the pro- 
positions in the order of Major Premiss, Minor Premiss, 

and Conclusion. Thus, the Second Figure being qj^ 
FEx/I;^0 is written—- 

No P is in M. 

Some S is in M. 

Some S is not in P. 

PM 
The Fourth Figure being ^g DlmArls is 

Some P is in M« 
All M is in S. 
Some S is in P. 

The initial letter in a Minor Mood indicates that 
Mood of the First to which it may be reduced. Thus 
Festino is reduced to Ferio, and Dimaris to Darii. In 
the cases of Baroko and Bokardo, B indicates that you 
may employ Barbara to bring any impugner to con- 
fusion, as shall be afterwards explained. 

The letters x, m, and p are also significant. Placed 
after a vowel, s indicates that the proposition has to be 
simply converted. Thus, FEstlnO :~ 

No P is in M. 

Some S is in M« 

Some S is not in P. 



Figures and Moods of the Syllogism, 179 

Simply convert the Major Premiss, and you get FErlO, 
of the First. 

No M is in P. 

Some S is in M. 

Some S is not in P. 

m (muta^ or move) indicates that the premisses have 
to be transposed. Thus, in CAwEj/rEj, you have to 
transpose the premisses, as well as simply convert the 
Minor Premiss before reaching the figure of CE/ArE«/. 

All P is in M ^ No M is in S 
No S is in M ^ All P is in M, 

From this it follows in CElArEnt that No P is in S, 
and this simply converted yields No S is in P. 

A simple transposition of the premisses in DImArls 
of the Fourth 

Some P is in M 

All M is in S 

yields the premisses of DArll 

All M is in S 
Some P is in Mj 

but the conclusion Some P is in S has to be simply 
converted. 

Placed after a vowel, p indicates that the proposition 
has to be converted per accidens. Thus in FE/A//0« 
oftheThird(MP, MS) 

No M is in P 
All M is in S 
Some S is not in P 

you have to substitute for All M is in S its converse 
by limitation to get the premisses of FEf 10. 



i8o The Interdependence of Proposfttons, 

Two of the Minor Moods, Baroko of the Second 
Figure, and Bokardo of the Third, cannot be reduced 
to the First Figure by the ordinary processes of Conver- 
sion and Transposition. It is for dealing with these 
intractable moods that Contraposition is required. 
Thus in BhrOkO of the Second (PM, SM) 

All P is in M. 
Some S is not in M. 

Substitute for the Major Premiss its Converse by 
Contraposition, and for the Minor its Formal Obverse 
or Permutation, and you have FErlO of the First, 
with not-M as the Middle. 

No not-M is in P. 
Some S is in not-M* 
Some S is not in F« 

The processes might be indicated by the Mnemonic 
YkcsOcOy with c indicating the contraposition of the 
predicate term or Formal Obversion. 
The reduction of BOMrrfO, 

Some M is not in P 
All M is in S 
Some S is not in P, 

is somewhat more intricate. It may be indicated by 
T>OcsKmOsc. You substitute for the Major Premiss 
its Converse by Contraposition, transpose the Pre- 
misses, and you have DArll. 

All M is in S. 
Some not-P is in M« 
Some not-P is in S» 



Figures and Mcrnds of the Syllogism. i8i 

Convert now the conclusion by Contraposition, and 
you have Some S is not in P. 

The author of the Mnemonic apparently did not 
recognise Contraposition, though it was admitted by 
Boethius; and, it being impossible without this to 
demonstrate the validity of Baroko and Bokardo by 
showing them to be equivalent with valid moods of 
the First Figure, he provided for their demonstration 
by the special process known as Reductio ad absurdum. 
B indicates that Barbara is the medium. 

The rationale of the process is this. It is an imagi- 
nary opponent that you reduce to an absurdity or self- 
contradiction. You show that it is impossible with 
consistency to admit the premisses and at the same 
time deny the conclusion. For, let this be done ; let it 
be admitted as in ^KrOkO that, 

All P is in M 
Some S is not in 5f . 

but denied that Some S is not ia P. The denial of a 
proposition implies the admission of its Contradictory, 
If it is not true that Some S is not in P, it must be 
true that All S is in P. Take this along with the 
admission that All P is in M, and you have a syllogism 
in BA^Mz-A, 

All P is in M 
All S is in P, 

yielding the conclusion All S is in M, If then the 
original conclusion is denied, it follows that All S is 
in M. But this contradicts the Minor Premiss, which 
has been admitted to be true. It is thus shown that 



tSa The Interdependence of Propositions* 

an opponent cannot admit the premisses and deny the 
conclusion without contradicting himself. 

The same process may be applied to Bokardo. 

Some M is not in P. 
All M is in S. 
Some S is not in P. 

Deny the conclusion, and you must admit that All 
S is in P. Syllogised in Barbara with All M is in S, 
this yields the conclusion that All M is in P, the 
contradictory of the Major Premiss. 

The beginner may be reminded that the argument 
ad ahsurdum is not necessarily confined to Baroko and 
Bokardo. It is applied to them simply because they 
are not reducible by the ordinary processes to the First 
Figure. It might be applied with equal effect to 
other Moods, jyimkrlsy e,g,^ of the Third. 

Some M is in P» 
All M is in S. 
Some S is in P. 

Let Some S is in P be denied, and No S is in P must 
be admitted. But if No S is in P and All M is in S, 
it follows (in Celarent) that No M is in P, which an 
opponent cannot hold consistently with his admission 
that Some M is in P. 

The beginner sometimes asks : What is the use of 
reducing the Minor Figures to the First ? The reason 
is that it is only when the relations between the terms 
are stated in the First Figure that it is at once appa- 
rent whether or not the argument is valid under the 
Axiom or Dictum de Omni, It is then undeniably 
evident that if the Dictum holds the argument holds. 



Figures and Moods of the Syllogism, 183 

And if the Moods of the First Figure hold, their 
equivalents in the other Figures must hold too, 

Aristotle recognised only two of the Minor Figures, 
the Second and Third, and thus had in all only fourteen 
valid moods. 

The recognition of the Fourth Figure is attributed 
by Averroes to Galen. Averroes himself rejects it on 
the ground that no arguments expressed naturally, 
that is, in accordance with common usage, fall into 
that form. This is a sufficient reason for not spending 
time upon it, if Logic is conceived as a science that 
has a bearing upon the actual practice of discussion or 
discursive thought. And this was probably the reason 
why Aristotle passed it over. 

If however the Syllogism of Terms is to be com- 
pleted as an abstract doctrine, the Fourth Figure must 
be noticed as one of the forms of premisses that contain 
the required relation between the extremes. There is 
a valid syllogism between the extremes when the 
relations of the three terms are as stated in certain 
premisses of the Fourth Figure. 

III. — The Sorites. 

A chain of Syllogisms is called a Sorites, Thus :— 

All A is in B. 
All B is in C. 
All C is in D, 



All X is in Z. 
.-. All A is in Z. 

A Minor Premiss can thus be carried through a 



184 The Interdependence of Proposiiions. 

series of Universal Propositions each serving in turn 
as a Major to yield a conclusion Vv^hich can be syllo- 
gised with the next. Obviously a Sorites may contain 
one particular premiss, provided it is the first; and 
one universal negative premiss, provided it is the last. 
A particular or a negative at any other point in the 
chain is an insuperable bar. 



CUArtER III. 

THE DEMONSTRATION OF THE SYLLOGISTIC MOODS. 
—THE CANONS OF THE SYLLOGISM. 

How do we know that the nineteen moods are the 
only possible forms of valid syllogism ? 

Aristotle treated this as being self-evident upon trial 
and simple inspection of all possible forms in each of 
his three Figures. 

Granted the parity between predication and position 
in or out of a limited enclosure (term, opos), it is a 
matter of the simplest possible reasoning. You have 
three such terms or enclosures, S, P and M ; and you 
are given the relative positions of two of them to the 
third as a clue to their relative positions to one 
another. Is S in or out of P, and is it wholly in or 
wholly out or partly in or partly out ? You know how 
each of them lies towards the third : when can you 
tell from this how S lies towards P ? 

We have seen that when M is wholly in or out of P, 
and S wholly or partly in M, S is wholly or partly in 
or out of P. 

Try any other given positions in the First Figure, 
and you find that you cannot tell from them how S 
lies relatively to P. Unless the Major Premiss is 
Universal, that is, unless M lies wholly in or out of P^ 
you can draw no conclusion, whatever the Minor 

(i8s) 



1 86 The Interdependence of Propositions, 

Premiss may give. Given, ^^., All S is in M, it may 
be that All S is in P, or that No S is in P, or that 
Some S is in P, or that Some S is not in P, 




Again, unless the Minor Premiss is affirmative, no 
matter what the Major Premiss may be, you can draw 
no conclusion. For if the Minor Premiss is negative, 
all that you know is that All S or Some S lies some- 
where outside M ; and however M may be situated 
relatively to P, that knowledge cannot help towards 
knowing how S lies relatively to P. All S may be P, 
or none of it, or part of it. Given all M is in P ; the 
All S (or Some S) which we know to be outside of M 
may lie anywhere in P or out of it. 




Similarly, in the Second Figure, trial and simple 
inspection of all possible conditions shows that there 
can be no conclusion unless the Major Premiss is 
universal, and one of the premisses negative. 

Another and more common way of eliminating the 
invalid forms, elaborated in the Middle Ages, is to 
formulate principles applicable irrespective of Figure, 



The Demonstration of the Syllogistic Moods^ 187 

and to rule out of each Figure the moods that do not 
conform to them. These regulative principles are 
known as The Canons of the Syllogism. 

Canon L In every syllogism there should be three, 
and not more than three, terms, and the terms must 
be used throughout in the same sense. 

It sometimes happens, owing to the ambiguity of 
words, that there seem to be three terms when there 
are really four. An instance of this is seen in the 
sophism : — 

He who is most hungry eats most. 
He who eats least is most hungry. 
.*. He who eats least eats most. 

This Canon, however, though it points to a real danger 
of error in the application of the syllogism to actual 
propositions, is superfluous in the consideration of 
purely formal implication, it being a primary assump- 
tion that terms are univocal, and remain constant 
through any process of inference. 

Under this Canon, Mark Duncan says (Inst, Log,^ 
iv. 3, 2), is comprehended another commonly expressed 
in this form : There should be nothing in the con- 
clusion that was not in the premisses : inasmuch as if 
there were anything in the conclusion that was in 
neither of the premisses, there would be four terms in 
the syllogism. 

The rule that in every syllogism there must be 
three, and only three, propositions, sometimes given 
as a separate Canon, is only a corollary from Canon I. 

Canon II. The Middle Term must be distributed 
once at least in the Premisses. 

The Middle Term must either be wholly in, or 
wholly out of, one or other of the Extremes before 



1 88 The Interdependence of Propositions, 

it can be the means of establishing a connexion 
between them. If you know only that it is partly in 
both, you cannot know from that how they lie relatively 
to one another : and similarly if you know only that it 
is partly outside both. 

The Canon of Distributed Middle is a sort of counter- 
relative supplement to the Dictum de Omni. Whatever 
is predicable of a whole distributively is predicable of 
all its several parts. If in neither premiss there is a 
predication about the whole, there is no case for the 
application of the axiom. 

Canon IIL No term should be distributed in the 
conclusion that was not distributed in the premisses. 

If an assertion is not made about the whole of a 
term in the premisses, it cannot be made about the 
whole of that term in the conclusion without going 
beyond what has been given. 

The breach of this rule in the case of the Major 
term is technically known as the Illicit Process of the 
Major : in the case of the Minor term, Illicit Process 
of the Minor. 

Great use is made of this canon in cutting off invalid 
moods. It must be remembered that the Predicate 
term is " distributed '' or taken universally in O (Some 
S is not in P) as well as in E (No S is in P) ; and 
that P is never distributed in affirmative propositions. 

Canon IV. No conclusion can be drawn from two 
negative premisses. 

Two negative premisses are really tantamount to a 
declaration that there is no connexion whatever between 
the Major and the Minor (as quantified in the premisses) 
and the term common to both premisses ; in short, that 
this is not a Middle term-— that the condition of a valid 
Syllogism does not exist. 



The Demonstration of the Syllogistic Moods. 189 

There is an apparent exception to this when the 
real Middle in an argument is a contrapositive term, 
not-M. Thus:— 

Nobody who is not thirsty is suffering from fever. 
This person is not thirsty. 
.*. He is not suffering from fever. 

But in such cases it is really the absence of a quality 
or rather the presence of an opposite quality on which 
we reason ; and the Minor Premiss is really Affirmative 
of the form S is in not-M. 

Canon V. If one premiss is negative, the conclusion 
must be negative. 

If one premiss is negative, one of the Extremes 
must be excluded in whole or in part from the Middle 
term. The other must therefore (under Canon IV.) 
declare some coincidence between the Middle term and 
the other extreme ; and the conclusion can only affirm 
exclusion in whole or in part from the area of this 
coincidence. 

Canon VL No conclusion can be drawn from two 
particular premisses. 

This is evident upon a comparison of terms in all 
possible positions, but it can be more easily demon- 
strated with the help of the preceding canons. The 
premisses cannot both be particular and yield a con- 
clusion without breaking one or other of those canons. 

Suppose both are affirmative, II, the Middle is not 
distributed in either premiss. 

Suppose one affirmative and the other negative, 10, 
or 01. Then, whatever the Figure may be, that is, 
whatever the order of the terms, only one term can be 
distributed, namely, the predicate of O. This (Canon 
11.) must be the Middle. But in that case there must 



T90 The Interdependence of Propositions. 

be Illicit Process of the Major (Canon III.), for one of 
the premisses being negative, the conclusion is negative 
(Canon V.), and P its predicate is distributed. Briefly, 
in a negative mood, both Major and Middle must be 
distributed, and if both premisses are particular this 
cannot be. 

Canon VIL If one Premiss is particular the con- 
clusion is particular. 

This canon is sometimes combined with what we 
have given as Canon V., in a single rule : " The 
conclusion follows the weaker premiss ". 

It can most compendiously be demonstrated with 
the help of the preceding canons. 

Suppose both premisses affirmative, then, if one is 
particular, only one term can be distributed in the 
premisses, namely, the subject of the Universal 
affirmative premiss. By Canon IL, this must be the 
Middle, and the Minor, being undistributed in the 
Premisses, cannot be distributed in the conclusion. 
That is, the conclusion cannot be Universal — must be 
particular. 

Suppose one Premiss negative, the other affirmative. 
One premiss being negative, the conclusion must be 
negative, and P must be distributed in the conclusion. 
Before, then, the conclusion can be universal, all three 
terms, S, M, and P, must, by Canons II. and III., be 
distributed in the premisses. But whatever the Figure 
of the premisses, only two terms can be distributed. 
For if one of the Premisses be O, the other must be A, 
and if one of them is E, the other must be I. Hence 
the conclusion must be particular, otherwise there will 
be illicit process of the Minor, or of the Major, or of 
the Middle. 

The argument may be more briefly put as follows : 



The^ Demonstration of the Syllogistic Moods » 191 

In an affirmative mood, with one premiss particular, 
only one term can be distributed in the premisses, and 
this cannot be the Minor without leaving the Middle 
undistributed. In a negative mood, with one premiss 
particular, only two terms can be distributed, and the 
Minor cannot be one of them without leaving either 
the Middle or the Major undistributed. 

Armed with these canons, we can quickly determine, 
given any combination of three propositions in one of 
the Figures, whether it is or is not a valid Syllogism. 

Observe that though these canons hold for all the 
Figures, the Figure must be known, in all combinations 
containing A or O, before we can settle a question of 
validity by Canons II. and III., because the distribution 
of terms in A and O depends on their order in 
predication. 

Take AEE. In Fig. I.— 

All M is in P 
No S is in M 
No S is in P— 

the conclusion is invalid as involving an illicit process 
of the Major. P is distributed in the conclusion and 
not in the premisses. 
In Fig. II. AEE— 

All P is in M 
No S is in M 
No S is in P— 

the conclusion is valid (Camestres). 



IQ2 755^ Interdependence of Propositi&m. 

In Fig. IIL AEE— 

All M is in P 

No M is in S 
No S is in P-- 

the conclusion is invalid, there being illicit process of 
the Major. 

In Fig. IV. AEE is valid (Camenes). 

Take EIO. A little reflection shows that this com- 
bination is valid in all the Figures if in any, the dis- 
tribution of the terms in both cases not being affected 
by their order in predication. Both E and I are simply 
convertible. That the combination is valid is quickly 
seen if we remember that in negative moods both 
Major and Middle must be distributed, and that this is 
done by E. 

EIE is invalid, because you cannot have a universal 
conclusion with one premiss particular. 

All is valid in Fig. I. or Fig. III., and invalid in 
Figs. II. and IV., because M is the subject of A in I. 
and III. and predicate in II. and IV. 

OAO is valid only in Fig. III., because only in that 
Figure would this combination of premisses distribute 
both M and P. 

Simple exercises of this kind may be multiplied till 
all possible combinations are exhausted, and it is seen 
that only the recognised moods stand the test. 

If a more systematic way of demonstrating the valid 
moods is desired, the simplest method is to deduce 
from the Canons special rules for each Figure. Aristotle 
arrived at these special rules by simple inspection, but 
it is easier to deduce tnem. 



The Demonstration of the Syllogistic Moods. 193 

L In the First Figure, the Major Premiss must be 
Universal, and the Minor Premiss affirmative. 

To make this evident by the Canons, we bear in 
mind the Scheme or Figure — 

M in P 
S in M— 

and try the alternatives of Affirmative Moods and 
Negative Moods. Obviously in an affirmative mood 
the Middle is undistributed unless the Major Premiss 
is Universal. In a negative mood, (i) If the Major 
Premiss is O, the Minor must be affirmative, and M is 
undistributed ; (2) if the Major Premiss is I, M may 
be distributed by a negative Minor Premiss, but in 
that case there would be an illicit process of the Major 
— P being distributed in the conclusion (Canon V.) and 
not in the Premisses. Thus the Major Premiss can 
neither be O nor I, and must therefore be either A or 
E, ix.y must be Universal. 

That the Minor must be affirmative is evident, for if 
it were negative, the conclusion must be negative 
(Canon V.) and the Major Premiss must be affirmative 
(Canon IV.), and this would involve illicit process of 
the Major, P being distributed in the conclusion and 
not in the Premisses. 

These two special rules leave only four possible 
valid forms in the First Figure. There are sixteen 
possible combinations of premisses, each of the four 
types of proposition being combinable with itself and 
with each of the others. 



AA 


EA 


lA 


OA 


AE 


EE 


IE 


OE 


AI 


EI 


II 


01 


AO 


EO 


10 


00 



la 



194 2%^ Interdependence of Propositions. 

Special Rule I. wipes out the columns on the right, 
with the particular major premisses; and AE, EE, 
AO, and EO are rejected by Special Rule 11. , leaving 
BArMrA, CE/A/-E«/, DArll and FErlO. 

II. In the Second Figure, only Negative Moods 
are possible, and the Major Premiss must be universal. 

Only Negative moods are possible, for unless one 
premiss is negative, M being the predicate term in 
both— 

P in M 

S in M— 

is undistributed. 

Only negative moods being possible, there will be 
illicit process of the Major unless the Major Premiss 
is universal, P being its subject term. 

These special rules reject AA and AI, and the two 
columns on the right. 

To get rid of EE and EO, we must call in the 
general Canon IV. ; which leaves us with EA, AE, 
EI, and AO — CE^ArE, Q^km^str'&s, FEj/I«0, 
BArOiiO. 

III. In the Third Figure, the Minor Premiss must 
be affirmative. 

Otherwise, the conclusion would be negative, and 
the Major Premiss affirmative, and there would be 
illicit process of the Major, P being the predicate term 
in the Major Premiss. 

M in P 
M in S. 

This cuts off AE, EE, IE, OE, AO, EO, 10, 00,— 
the second and fourth rows in the above list. 

II and 01 are inadmissible by Canon VL ; which 



The Demonstration of the Syllogistic Moods. 195 

leaves AA, lA, AI, EA, OA, El— DArA//I, Dlskmls, 
DArtjI, FE/AptOn, BOMr^O, FErlxO—three affir- 
mative moods and three negative. 

IV. The Fourth Figure is fenced by three special 
rules, (i) In negative moods, the Major Premiss is 
universal. (2) If the Minor is negative, both premisses 
are universal. (3) If the Major is affirmative, the 
Minor is universal. 

(i) Otherwise, the Figure being 

PinM 
M in S, 

there would be illicit process of the Major. 

(2) The Major must be universal by special rule (i), 
and if the Minor were not also universal, the Middle 
would be undistributed. 

(3) Otherwise M would be undistributed. 
Rule (i) cuts off the right-hand column j OA, OE, 

01, and 00 ; also IE and 10. 

Rule (2) cuts off AO, EO. 

Rule (3) cuts off AI, II. 

EE goes by general Canon IV. ; and we are left 
with AA, AE, lA, EA, EI—BrAmAntlp, CAmEnEsy 
DlmArls, FE^A/O^ FrEslsO^. 



Chaftee W. 

THE ANALYSIS OF ARGUMENTS INTO SYLLOGISTIC 
FORMS. 

Turning given arguments into syllogistic form is apt 
to seem as trivial and useless as it is easy and 
mechanical. In most cases the necessity of the con- 
clusion is as apparent in the plain speech form as in 
the artificial logical form. The justification of such 
exercises is that they give familiarity with the instru- 
ment, serving at the same time as simple exercises in 
ratiocination : what further uses may be made of the 
instrument once it is mastered, we shall consider as 
we proceed. 

L — First Figure, 

Given the following argument to be put into Syllo- 
gistic form : " No war is long popular : for every war 
increases taxation ; and the popularity of anything 
that touches the pocket is short-lived ". 

The simplest method is to begin with the conclusion 
— " No war is long popular " — No S is P — then to 
examine the argument to see whether it yields premisses 
of the necessary form. Keeping the form in mind, 
Celarent of Fig. L — 

No M is P 
All S is M 
No S is P— 
(196) 



The Analysis of Arguments into Syllogistic Forms. 197 

we see at once that " Every war increases taxation " is 
of the form All S is M. Does the other sentence yield 
the Major Premiss No M is P, when M represents the 
increasing of taxation, i>., a class bounded by that 
attribute ? We see that the last sentence of the argu- 
ment is equivalent to saying that " Nothing that 
increases taxation is long popular " ; and this with the 
Minor yields the conclusion in Celarent. 

Nothing that increases taxation is long popular. 
Every war increases taxation. 
No war is long popular. 

Observe, now, what in effect we have done in thus 
reducing the argument to the First Figure. In effect, 
a general principle being alleged as justifying a certain 
conclusion, we have put that principle into such a form 
that it has the same predicate with the conclusion. 
All that we have then to do in order to inspect the 
validity of the argument is to see whether the subject 
of the conclusion is contained in the subject of the 
general principle. Is war one of the things that 
increase taxation ? Is it one of that class ? If so, 
then it cannot long be popular, long popularity being 
an attribute that cannot be affirmed of any of that 
class. 

Reducing to the first figure, then, amounts simply 
to making the predication of the proposition alleged 
as ground uniform with the conclusion based upon it. 
The minor premiss or applying proposition amounts to 
saying that the subject of the conclusion is contained in 
the subject of the general principle. Is the subject of 
the conclusion contained in the subject of the general 
principle when the two have identical predicates ? If 



198 The Interdependence of Propositions. 

so, the argument falls at once under the Dictum de 
Omni et Nulla. 

Two things may be noted concerning an argument 
thus simplified. 

1. It is not necessary, in order to bring an argument 
under the dictum de omni^ to reduce the predicate to the 
form of an extensive term. In whatever form, abstract 
or concrete, the predication is made of the middle term, 
it is applicable in the same form to that which is con- 
tained in the middle term. 

2. The quantity of the Minor Term does not require 
special attention, inasmuch as the argument does not 
turn upon it. In whatever quantity it is contained in 
the Middle, in that quantity is the predicate of the 
Middle predicable of it. 

These two points being borne in mind, the attention 
may be concentrated on the Middle Term and its 
relations with the extremes. 

That the predicate may be left unanalysed without 
affecting the simplicity of the argument or in any way 
obscuring the exhibition of its turning-point, has an 
important bearing on the reduction of Modals. The 
modality may be treated as part of the predicate without 
in any way obscuring what it is the design of the syllo- 
gism to make clear. We have only to bear in mind that 
however the predicate may be qualified in the pre- 
misses, the same qualification must be transferred to 
the conclusion. Otherwise we should have the fallacy 
of Four Terms, quaternio terminorum. 

To raise the question : What is the proper form for 
a Modal of Possibility, A or I ? is to clear up in an 
important respect our conceptions of the Universal 
proposition, " Victories may be gained by accident ". 



The Analysis of Arguments into Syllogistic Forms, 199 

Should this be expressed as A or I ? Is the predicate 
applicable to All victories or only to Some ? Obviously 
the meaning is that of any victory it may be true that 
it was gained by accident, and if we treat the " mode " 
as part of the predicate term " things that may be 
gained by accident," the form of the proposition is All 
S is in P. 

But, it may be asked, does not the proposition that 
victories may be gained by accident rest, as a matter 
of fact, on the belief that some victories have been 
gained in this way ? And is not, therefore, the propel 
form of proposition Some S is P ? 

This, however, is a misunderstanding. What we 
are concerned with is the formal analysis of proposi- 
tions as given. And Some victories have been gained 
by accident is not the formal analysis of Victories may 
be gained by accident. The two propositions do not 
give the same meaning in different forms : the meaning 
as well as the form is different. The one is a statement 
of a matter of fact : the other of an inference founded 
on it. The full significance of the Modal proper may 
be stated thus : In view of the fact that some victories 
have been gained by accident, we are entitled to say ot 
any victory, in the absence of certain knowledge, that 
it may be one of them. 

A general proposition, in short, is a proposition 
about a genus, taken universally. 

II. — Second Figure. 

For testing arguments from general principles, the 
First Figure is the simplest and best form of analysis. 

But there is one common class of arguments that 
fell naturally, as ordinarily expressed, into the Second 



206 iTie interdependence of ProposiHons, 

Figure, namely, negative conclusions from the absence 
of distinctive signs or symptoms, or necessary con- 
ditions. 

Thirst, for example, is one of the symptoms of fever : 
if a patient is not thirsty, you can conclude at once 
that his illness is not fever, and the argument, fully 
expressed, is in the Second Figure. 

All fever-stricken patients are thirsty. 
This patient is not thirsty. 
•*• He is not fever-stricken. 

Arguments of this type are extremely common. 
Armed with the general principle that ill-doers are ill- 
dreaders, we argue from a man's being unsuspicious 
that he is not guilty. The negative diagnosis of the 
physician, as when he argues from the absence of sore 
throat or the absence of a white speck in the throat 
that the case before him is not one of scarlatina or 
diphtheria, follows this type: and from its utility in 
making such arguments explicit, the Second Figure 
may be called the Figure of Negative Diagnosis. 

It is to be observed, however, that the character of 
the argument is best disclosed when the Major Premiss 
is expressed by its Converse by Contraposition. It 
is really from the absence of a symptom that the 
physician concludes ; as, for example : " No patient 
that has not a sore throat is suffering from scarlatina ". 
And the argument thus expressed is in the First 
Figure. Thus the reduction of Baroko to the First 
Figure by contraposition of the Middle is vindicated as 
a really useful process. The real Middle is a contra- 
positive term, and the form corresponds more closely 
to the reasoning when the argument is put in the First 
Figure. 



The Analysis of Arguments into Syllogistic Forms. 201 

The truth is that if the positive term or sign or 
necessary condition is prominent as the basis of the 
argument, there is considerable risk of fallacy. Sore 
throat being one of the symptoms of scarlatina, the 
physician is apt on finding this symptom present to 
jump to a positive conclusion. This is equivalent 
technically to drawing a positive conclusion from 
premisses of the Second Figure. 

All scarlatina patients have sore throat. 
This patient has sore throat. 

A positive conclusion here is technically known as a 
Non-Sequitur (Doesn't follow). So with arguments 
from the presence of a necessary condition which is 
only one of many. Given that it is impossible to pass 
without working at the subject, or that it is impossible 
to be a good marksman without having a steady hand, 
we are apt to argue that given also the presence of this 
condition, a conclusion is implicated. But really the 
premisses given are only two affirmatives of the 
Second Figure. 

"It is impossible to pass without working at the sub- 
ject" 

This, put into the form No not-M is P, is to say that 
'* None who have not worked can pass ". This is 
equivalent, as the converse by contraposition, with — 

All capable of passing have worked at the subject. 

But though Q has worked at the subject, it does not 
follow that he is capable of passing. Technically the 
middle is undistributed. On the other hand, if he has 
not worked at the subject, it follows that he is not 
capable of passing. We can draw a conclusion at 



202 The Interdependence of Propositions. 

once from the absence of the necessary condition, 
though none can be drawn from its presence alone. 

Third Figure. 

Arguments are sometimes advanced in the form 
of the Third Figure. For instance : Killing is not 
always murder: for tyrannicide is not murder, and 
yet it is undoubtedly killing. Or again : Unpleasant 
things are sometimes salutary: for afflictions are 
sometimes so, and no affliction can be called pleasant. 

These arguments, when analysed into terms, are, 
respectively, Felapton and Disamis. 

No tyrannicide is murder ; 
All tyrannicide is killing ; 
Some killing is not murder. 

Some afflictions are salutary things ; 
All afflictions are unpleasant things ; 
Some unpleasant things are salutary things. 

The syllogistic form cannot in such cases pretend to 
be a simplification of the argument. The argument 
would be equally unmistakable if advanced in this 
form: Some S is not P, for example, M. Some 
killing is not murder, e.g.^ tyrannicide. Some un- 
pleasant things are salutary, e,g.^ some afflictions. 

There is really no ** deduction " in the third figure, 
no leading down from general to particular. The 
middle term is only an example of the minor. It is 
the syllogism of Contradictory Examples. 

In actual debate examples are produced to disprove 
a universal assertion, afflrmative or negative. Suppose 
it is maintained that every wise man has a keen sense 
of humour. You doubt this : you produce an instance 
of the opposite, say Milton. The force of your contra- 
dictory instance is not increased by exhibiting the 



The Analysis of Argmnents into Syllogistic Forms, 203 

argument in syllogistic form : the point is not made 
clearer. 

The Third Figure was perhaps of some use in Yes 
and No Dialectic. When you had to get everything 
essential to your conclusion definitely admitted, it was 
useful to know that the production of an example to 
refute a generality involved the admission of two 
propositions. You must extract from your opponent 
both that Milton was a wise man, and that Milton had 
not a keen sense of humour, before you could drive 
him from the position that all wise men possess that 
quality. 

Examples for Analysis. 

Scarlet flowers have no fragrance: this flower has no 
fragrance: does it follow that this flower is of a scarlet 
colour ? 

Interest in the subject is an indispensable condition ol 
learning easily : Z is interested in the subject : he is bound, 
therefore, to learn easily. 

It is impossible to be a good shot without having a steady 
hand : John has a steady hand : he is capable, therefore, of 
becoming a good shot. 

Some victories have been won by accident ; for example, 
Mai wand. 

Intemperance is more disgraceful than cowardice, be- 
cause people have more opportunities of acquiring control 
of their bodily appetites. 

"Some men are not fools, yet all men are fallible." 
What follows ? 

" Some men allow that their memory is not good : every 
man believes in his own judgment.*' What is the con- 
clusion, and in what Figure and Mood may the argument 
be expressed ? 

" An honest man's the noblest work of God : Z is an 
honest man ** : therefore, he is — what ? 

Examine the logical connexion between the following 



204 The Interdependence of Propositions, 

"exclamation" and "answer": "But I hear some one 
exclaiming that wickedness is not easily concealed. To 
which I answer, Nothing great is easy." 

" If the attention is actively aroused, sleep becomes 
impossible : hence the sleeplessness of anxiety, for anxiety 
is a strained attention upon an impending disaster." 

" To follow truth can never be a subject of regret ; free 
inquiry does lead a man to regret the days of his childish 
faith ; therefore it is not following truth." — J, H. Newman, 

He would not take the crown : Therefore 'tis certain he 
was not ambitious. 

As he was valiant, I honour him ; as he was ambitious, I 
slew him. 

The Utopians learned the language of the Greeks with 
more readiness because they were originally of the same 
race with them. 

Nothing which is cruel can be expedient, for cruelty is 
most revolting to the nature of man. 

"The fifth century saw the foundation of the Frank 
dominion in Gaul, and the first establishment of the German 
races in Britain. The former was effected in a single long 
reign, by the energy of one great ruling tribe, which had 
already modified its traditional usages, and now, by the 
adoption of the language and religion of the conquered, 
prepared the way for a permanent amalgamation with 
them." In the second of the above sentences a general 
proposition is assumed. Show in syllogistic form how the 
last proposition in the sentence depends upon it. 

" I do not mean to contend that active benevolence may 
not hinder a man's advancement in the world : for advance- 
ment greatly depends upon a reputation for excellence in 
some one thing of which the world perceives that it has 
present need: and an obvious attention to other things, 
though perhaps not incompatible with the excellence itself, 
may easily prevent a person from obtaining a reputation for 
it." Pick out the propositions here given as interdependent 
Examine whether the principle alleged is sufficiently general 
to necessitate a conclusion. In what form would it be so ? 



Chapter ¥• 

ENTHYMEMES. 

There is a certain variety in the use of the word 
Enthymeme among logicians. In the narrowest 
sense, it is a valid formal syllogism, with one premiss 
suppressed. In the widest sense it is simply an argu- 
ment, valid or invalid, formal in expression or informal, 
with only one premiss put forward or hinted at, the 
other being held in the mind (cr 6vfii§), This last is 
the Aristotelian sense. 

It is only among formal logicians of the straitest 
sect that the narrowest sense prevails. Hamilton 
divides Enthymemes into three classes according as it 
is the Major Premiss, the Minor Premiss, or the Con- 
clusion that is suppressed. Thus, a full syllogism 
being : — 

All liars are cowards : 

Caius is a liar : 
•*. Caius is a coward :— » 

this may be enthymematically expressed in three ways. 

I. Enthymeme of the First Order (Major under- 
stood). 

Caius is a coward ; for Caius is a liar. 

II. Enthymeme of the Second Order {Minor under- 
stood). 

Caius is a coward ; for all liars are cowards« 
(205) 



2o6 The Interdependence of Propositions, 

III. Enthymeme of the Third Order {Conclusion 
understood). 

All liars are cowards, and Caius is a liar. 

The Third Order is a contribution of Hamilton's 
own. It is superfluous, inasmuch as the conclusion is 
never suppressed except as a rhetorical figure of speech. 
Hamilton confines the word Enthymeme to valid argu- 
ments, in pursuance of his view that Pure Logic has 
no concern with invalid arguments. 

Aristotle used Enthymeme in the wider sense of an 
elliptically expressed argument. There has been some 
doubt as to the meaning of his definition, but that 
disappears on consideration of his examples. He 
defines an Enthymeme (Prior Analyt., ii. 27) as " a 
syllogism from probabilities or signs " (cn;AAoyt(r/Aos c^ 
ctKOTCDv ri (n]fjL€LO)v). The word syllogism in this con- 
nexion is a little puzzling. But it is plain from the 
examples he gives that he meant here by syllogism not 
even a correct reasoning, much less a reasoning in the 
explicit form of three terms and three propositions. He 
used syllogism, in fact, in the same loose sense in which 
we use the words reasoning and argument, applying 
without distinction of good and bad. 

The sign, he says, is taken in three ways, in as 
many ways as there are Syllogistic Figures. 

(i) A sign interpreted in the First Figure is conclu- 
sive. Thus : " This person has been drowned, for he 
has froth in the trachea ". Taken in the First Figure 
with "All who have froth in the trachea have been 
drowned " as major premiss, this argument is valid. 
The sign is conclusive. 

(2) " This patient is fever-stricken, for he is thirsty,* 
Assumed that "All fever-stricken patients are thirsty ,** 



Enthymemes. 207 

this is an argument in the Second Figure, but it is not 
a valid argument. Thirst is a sign or symptom of 
fever, but not a conclusive sign, because it is indicative 
of other ailments also. Yet the argument has a certain 
probability. 

(3) '^ Wise men are earnest (o-irov&uoi), for Pittacus 
is earnest." Here the suppressed premiss is that 
" Pittacus is wise ". Fully expressed, the argument is 
in the Third Figure : — 

Pittacus is earnest. 
Pittacus is wise. 
.•. Wise men are earnest. 

Here again the argument is inconclusive and yet it 
has a certain probability. The coincidence of wisdom 
with earnestness in one notable example lends a 
certain air of probability to the general statement. 

Such are Aristotle's examples or strict parallels to 
them. The examples illustrate also what he says in 
his Rhetoric as to the advantages of enthymemes. For 
purposes of persuasion enthymemes are better than 
explicit syllogisms, because any inconclusiveness there 
may be in the argument is more likely to pass un- 
detected. As we shall see, one main use of the 
Syllogism is to force tacit assumptions into light and 
so make their true connexion or want of connexion 
apparent. In Logic enthymemes are recognised only 
to be shown up : the elliptical expression is a cover for 
fallacy, which it is the business of the logician to strip 
off 

In Aristotle's examples one of the premisses is 
expressed. But often the arguments of common 
speech are even less explicit than this. A general 
principle is vaguely hinted at : a subject is referred to 



2o8 The Interdependence of Propositions. 

a class the attributes of which are assumed to be 
definitely known. Thus : — 

He was too ambitious to be scrupulous in his choice of 

means. 
He was too impulsive not to have made many blunders. 

Each of these sentences contains a conclusion and an 
enthymematic argument in support of it. The hearer 
is understood to have in his mind a definite idea of the 
degree of ambition at which a man ceases to be 
scrupulous, or the degree of impulsiveness that is 
incompatible with accuracy. 

One form of enthymeme is so common in modern 
rhetoric as to deserve a distinctive name. It may be 
called theEnthymeme of the Abstractly Denominated 
Principle. A conclusion is declared to be at variance 
with the principles of Political Economy, or contrary 
to the doctrine of Evolution, or inconsistent with 
Heredity, or a violation of the sacred principle ol 
Freedom of Contract. It is assumed that the hearer is 
familiar with the principles referred to. As a safe- 
guard against fallacy, it may be well to make the 
principle explicit in a proposition uniform with the 
conclusion. 



Chapter VI. 

THE UTILITY OF THE SYLLOGISM. 

The main use of the Syllogism is in dealing with 
incompletely expressed or elliptical arguments from 
general principles. This may be called Enthymematic 
argument, understanding by Enthymeme an argument 
with only one premiss put forward or hinted at, the 
other being held in the mind. In order to test whether 
such reasoning is sound or unsound, it is of advantage 
to make the argument explicit in Syllogistic form. 

There have been heaps and mazes of discussion 
about the use of the Syllogism, much of it being 
profitable as a warning against the neglect of Formal 
Logic. Again and again it has been demonstrated 
that the Syllogism is useless for certain purposes, and 
from this it has been concluded that the Syllogism is 
of no use at all. 

The inventor of the Syllogism had a definite 
practical purpose, to get at the simplest, most con- 
vincing, undeniable and irresistible way of putting 
admitted or self-evident propositions so that their 
implication should be apparent. His ambition was to 
furnish a method for the Yes and No Dialectician, and 
the expounder of science from self-evident principles. 
A question being put up for discussion, it was an 
advantage to analyse it, and formulate the necessary 
14 (209) 



210 Hhe Interdependence of Propositions. 

premisses : you could then better direct your interroga- 
tions or guard your answers. The analysis is similarly 
useful when you want to construct an argument from 
self-evident principles. 

All that the Syllogism could show was the consis- 
tency of the premisses with the conclusion. The 
conclusion could not go beyond the premisses, because 
the questioner could not go beyond the admissions of 
the respondent. There is indeed an advance, but not 
an advance upon the two premisses taken together. 
There is an advance upon any one of them, and this 
advance is made with the help of the other. Both 
must be admitted : a respondent may admit one with- 
out being committed to the conclusion. Let him 
admit both and he cannot without self-contradiction 
deny the conclusion. That is all. 

Dialectic of the Yes and No kind is no longer 
practised. Does any analogous use for the Syllogism 
remain ? Is there a place for it as a safeguard against 
error in modern debate ? As a matter of fact it is 
probably more useful now than it* was for its original 
purpose, inasmuch as modern discussion, aiming at 
literary grace and spurning exact formality as smacking 
of scholasticism and pedantry, is much more flabby and 
confused. In the old dialectic play there was generally 
a clear question proposed. The interrogative form 
forced this much on the disputants. The modern 
debater of the unpedantic, unscholastic school is not 
so fettered, and may often be seen galloping wildly 
about without any game in sight or scent, his maxim 
being to — 

Spur boldly on, and dash through thick and thin, 
Through sense and nonsense, never out nor in. 



f%e Utility of the Syllogism. iii 

Now the syllogistic analysis may often be of some 
I use in helping us to keep a clear head in the face of a 
confused argument. There is a brilliant defence of 
the syllogism as an analysis of arguments in the West- 
minster Review for January, 1828. The article was a 
notice of Whately's Logic : it was written by J. S. 
Mill, For some reason it has never been reprinted, 
but it puts the utility of the Syllogism on clearer 
ground than Mill afterwards sought for it. 

Can a fallacy in argument be detected at once ? 
Is common-sense sufficient ? Common-sense would 
require some inspection. How would it proceed ? 
Does common-sense inspect the argument in a lump 
or piecemeal ? All at once or step by step ? It 
analyses. How ? First, it separates out the proposi- 
tions which contribute to the conclusion from those 
which do not, the essential from the irrelevant. Then 
it states explicitly all that may have been assumed 
tacitly. Finally, it enumerates the propositions in 
order. 

Some such procedure as this would be adopted by 
common-sense in analysing an argument. But when 
common-sense has done this, it has exhibited the 
argument in a series of syllogisms. 

Such is Mill's early defence of the Syllogism. It is 
weak only in one point, in failing to represent how 
common-sense would arrive at the peculiar syllogistic 
form. It is the peculiar form of logical analysis that 
is the distinction of the syllogism. When you have 
disentangled the relevant propositions you have not 
necessarily put them in this form. The arguments 
given in text-books to be cast into syllogistic form, 
consist only as a rule of relevant propositions, but they 
are not yet formal syllogisms. But common-sense 



212 The Interdependence of Propositions. 

had only one other step to make to reach the distinc- 
tive form. It had only to ask after analysing the 
argument, Is there any form of statement specially 
suitable for exhibiting the connexion between a con- 
clusion and the general principle on which it is alleged 
to depend ? Ask yourself the question, and you will 
soon see that there would be an obvious advantage in 
making the conclusion and the general principle 
uniform, in stating them with the same predicate. 
But when you do this, as I have already shown (p. 197) 
you state the argument in the First Figure of the 
Syllogism. 

It must, however, be admitted that it is chiefly for 
exhibiting, or forcing into light, tacit or lurking 
assumptions that the Syllogistic form is of use. 
Unless identity of meaning is disguised or distorted by 
puzzling difference of language, there is no special 
illuminative virtue in the Syllogism. The argument 
in a Euclidean demonstration would not be made 
clearer by being cast into formal Syllogisms. 

Again, when the subject matter is simple, the 
Syllogistic form is not really required for protection 
against error. In such enthymemes as the following 
for example : — 

She must be clever : she is so uncompromisingly ugly. 
Romeo must be in love : for is he not seventeen ? 

it is plain to the average intelligence without any 
knowledge of Syllogism that the argument takes for 
granted a general proposition and what the general 
proposition is. 

Another thing is plain to the average intelligence, 
perhaps plainer than to a proficient in the use of the 



The Utility of the Syllogism. ai3 

Syllogism. Clearly we cannot infer with certainty 
that a woman is clever because she is ugly, unless it 
is the case that all ugly women are clever. But a 
Syllogiser, seeing that no certain conclusion can be 
drawn except upon this condition, is apt to dismiss 
the argument as altogether worthless. This may be 
specified as an error incident to the practice of the 
Syllogism, that it inclines us to look for necessarily 
conclusive premisses, and to deny all weight to any- 
thing short of this. Now in ordinary life it is com- 
paratively seldom that such premisses can be found. 
We are obliged to proceed on maxims that are not of 
universal scope, and which lend only a more or less 
strong colour of probability to cases that can be brought 
under them. " A little learning is a dangerous thing ; " 
" Haste makes waste ; " " Slowness of speech is a sign 
of depth of thought;" "Vivacity is a sign of shallow- 
ness : '' such are the " endoxes " or commonplaces of 
popular knowledge that men bring to bear in daily life. 
They are not true for all cases, but some of them are true 
for most or for a good many, and they may be applied 
with a certain probability though they are not rigidly 
conclusive. The plain man's danger is that he apply 
them unthinkingly as universals : the formal logician's 
danger is that, seeing them to be inapplicable as uni- 
versals, he dismisses them as being void of all 
argumentative force. 

It helps to fix the limits of Formal Logic to remember 
that it lies outside its bounds to determine the degree 
of probability attaching to the application of approxi- 
mate truths, such as are the staple of arguments in 
ordinary affairs. Formal Logic, we may repeat, is 
not concerned with degrees of truth or falsehood, 
probability or improbability. It merely shows the 



314 2%^ Interdependence of Propositions* 

interdependency of certain arguments, the consistency 
of conclusion with premisses. 

This, however, is a function that might easily h% 
underrated. Its value is more indirect than direct. la 
showing what is required for a certain conclusion, it 
puts us on the road to a more exact estimate of the 
premisses alleged, a sounder judgment of their 
worth. Well begun is half done : in undertaking the 
examination of any argument from authority, a 
formal syllogism is a good beginnings 



Chapter VII. 

CONDITIONAL ARGUMENTS.— HYPOTHETICAL SYLLO- 
GISM, DISJUNCTIVE SYLLOGISM, AND DILEMMA. 

The justification of including these forms of argu- 
ment in Logic is simply that they are sometimes used 
in debate, and that confusion may arise unless the 
precise meaning of the premisses employed is under* 
stood. Aristotle did not include them as now given in 
his exposition of the Syllogism, probably because they 
have no connexion with the mode of reasoning together 
to which he appropriated the title. The fallacies con- 
nected with them are of such a simple kind that to 
discuss as a question of method the precise place they 
should occupy in a logical treatise is a waste of 
ingenuity.^ 

I. — Hypothetical Syllogisms. 

^ !^ ^ PONENS. 

.% C is D j 

If A is B, Cis D] TVT 
_ . ' _^ I Modus 
C IS not D y rj^ 

. . T^ TOLLENS. 

/. A IS not B J 

* For the history of Hypothetical Syllogism see ManseP^ 
Aldrichj Appendix I. 

("5) 



2i6 The Interdependence of Propositions. 

A so-called Hypothetical Syllogism is thus seen to 
be a Syllogism in which the major premiss is a 
Hypothetical Proposition, that is to say, a complex 
proposition in which two propositions are given as so 
related that the truth of one follows necessarily from 
the truth of the other. 

Two propositions so related aire technically called 
the Antecedent or Reason, and the Consequent. 

The meaning and implication of the form, If A is B, 
C is D, is expressed in what is known as the Law of 
Reason and Consequent : — 

" When two propositions are related as Reason and 
Consequent^ the truth of the Consequent follows from the 
truth of the Antecedent ^ and the falsehood of the Antecedent^ 
from the falsehood of the Consequent ^\ 

If A is B, C is D, implies that If C is not D, A is 
not B. If this subject is educative, it quickens the 
wits ; if it does not quicken the wits, it is not educa- 
tive. 

Admitted, then, that the law of Reason and Conse- 
quent holds between two propositions — that If A is B, 
C is D: admitted also the Antecedent, the truth of 
the Consequent follows. This is the Modus Ponens 
or Positive Mode, where you reach a conclusion by 
obtaining the admission of the Antecedent. Admit the 
Antecedent and the truth of the Consequent follows. 

With the same Major Premiss, you may also, under 
the Law of Reason and Consequent reach a conclusion 
by obtaining the denial of the Consequent. This is 
the Modus ToUens or Negative Mode. Deny the Con- 
sequent and one is bound to deny the Antecedent. 

But to guard against the fallacy technically known 
as Fallacia Consequentis, we must observe what the 
relation of Reason and Consequent does not imply. 



Conditional Arguments. ai7 

The truth of the Consequent does not involve the 
truth of the Antecedent, and the falsehood of the Ante- 
cedent does not involve the falsehood of the Conse- 
quent. 

'' If the harbour is frozen, the ships cannot come 
in." If the harbour is not frozen, it does not follow 
that the ships can come in : they may be excluded by 
other causes. And so, though they cannot come in, it 
does not follow that the harbour is frozen. 
Questions Connected with Hypothetical Syllogisms. 

(i) Are they properly called Syllogisms 1 This is 
purely a question of Method and Definition. If we 
want a separate technical name for forms of argument 
in which two terms are reasoned together by means of 
a third, the Hypothetical Syllogism, not being in such 
a form, is not properly so called. The fact is that for 
the purposes of the Hypothetical Argument, we do not 
require an analysis into terms at all : it is superfluous : 
we are concerned only with the affirmation or denial of 
the constituent propositions as wholes. 

But if we extend the word Syllogism to cover all 
arguments in which two propositions necessarily 
involve a third, the Hypothetical Argument is on this 
understanding properly enough called a Syllogism. 

(2) Is the inference in the Hypothetical Syllogism 
Mediate or Immediate t 

To answer this question we have to consider whether 
the Conclusion can be drawn from either of the two 
premisses without the help of the other. If it is 
possible immediately, it must be educible directly 
either from the Major Premiss or from the Minor. 

(a) Some logicians argue as if the Conclusion were 
immediately possible from the Major Premiss. The 
Minor Premiss and the Conclusion, they urge, are 



2i8 The Interdependence of Propositions, 

simply equivalent to the Major Premiss. But this is 
a misunderstanding. " If A is B, C is D," is not 
equivalent to *' A is B, therefore C is D ". " If the 
harbour is frozen, the ships cannot come in " is not to 
say that "the harbour is frozen, and therefore," etc. 
The Major Premiss merely affirms the existence of the 
relation of Reason and Consequent between the two 
propositions. But we cannot thereupon assert the 
Conclusion unless the Minor Premiss is also conceded : 
that is, the inference of the Conclusion is Mediate, 
as being from two premisses and not from one 
alone. 

{t) Similarly with Hamilton's contention that the 
Conclusion is inferrible immediately from the Minor 
Premiss, inasmuch as the Consequent is involved in 
the Reason. True, the Consequent is involved in the 
Reason : but we cannot infer from " A is B '* to " C is 
D," unless it is conceded that the relation of Reason 
and Consequent holds between them ; that is, unless 
the Major Premiss is conceded as well as the Minor. 

(3) Can Hypothetical Syllogisms be reduced to the 
Categorical Form ? 

To oppose Hypothetical Syllogisms to Categorical 
is misleading, unless we take note of the precise 
difference between them. It is only in the form of the 
Major Premiss that they differ: Minor Premiss and 
Conclusion are categorical in both. And the meaning 
of a Hypothetical Major Premiss (unless it is a mere 
arbitrary convention between two disputants, to the 
effect that the Consequent will be admitted if the 
Antecedent is proved, or that the Antecedent will be 
relinquished if the Consequent is disproved), can 
always be put in the form pf a general proposition, 
from which, with the Minor Premiss as applying 



Conditional Arguments. 219 

proposition, a conclusion identical with the original 
can be drawn in regular Categorical form. 
Thus:— 

If the harbour is frozen, the ships cannot come in. 
The harbour is frozen. 
•*. The ships cannot come in. 

This is a Hypothetical Syllogism, Modus Ponens. 
Express the Hypothetical Major in the form of the 
general proposition which it implies, and you reach a 
conclusion (in Barbara) which is only grammatically 
different from the original. 

All frozen harbours exclude ships. 
The harbour is frozen. 
.'. It excludes ships. 

Again, take an example of the Modus Tolkm-^ 

If rain has fallen, the streets are weL 
The streets are not wet. 
.'. Rain has not fallen. 

This is reducible, by formulating the underlying 
proposition, to Camestres or Baroko of the Second 
Figure. 

All streets rained upon are wet 

The streets are not wet. 
.•. They are not streets rained upon. 

Hypothetical Syllogisms are thus reducible, by 
merely grammatical change,^ or by the statement of 

1 It may be argued that the change is not merely grammatical, 
and that the implication of a general proposition in a hypothetical 
and vice versd is a strictly logical concern. At any rate such an 
implication exists, whether it is the function of the Grammarian 
or the Logician to expound it. 



220 The Interdependence of Propontion$. 

self-evident implications, to the Categorical form. 
And, similarly, any Categorical Syllogism may be 
reduced to the Hypothetical form. Thus: — 

All men are mortal* 
Socrates is a man. 
.*• Socrates is mortaL 

This argument is not different, except in the expression 
of the Major and the Conclusion, from the following \' — 

If Socrates is a man, death will overtake him. 
Socrates is a man. 
.•• Death will overtake him. 

The advantage of the Hypothetical form in argument 
is that it is simpler. It was much used in Mediaeval 
Disputation, and is still more popular than the 
Categorical Syllogism. Perhaps the prominence givet 
to Hypothetical Syllogisms as syllogisms in Post- 
Renaissance text-books is due to the use of them in 
the formal disputations of graduands in the Universities. 
It was the custom for the Disputant to expound his 
argument in this form : — 

If so and so is the case, such and such follows. 
So and so is the case. 
.*• Such and such follows. 

To which the Respondent would reply: Acdpio 
antecedenteniy nego consequentiam^ and argue accordingly, 
Petrus Hispanus does not give the Hypothetical 
Syllogism as a Syllogism : he merely explains the true 
law of Reason and Consequent in connexion with the 
Fallacia Consequentis in the section on Fallacies. 
{Summulce. Tractatus Sextus.) 



Conditional Arguments. %t\ 

II. — Disjunctive Syllogisms. 

A Disjunctive Syllogism is a syllogism in which the 
Major Premiss is a DisjunctiYe Proposition, i.e., one 
in which two propositions are declared to be mutually 
incompatible. It is of the form Either A is B, or C is 
D.i 

If the disjunction between the alternatives is really 
complete, the form implies four hypothetical proposi- 
tions :— 

(i) If A is B, C is not D. 

(2) If A is not B, C is D. 

(3) If C is D, A is not B, 

(4) If C is not D, A is B. 

Suppose then that an antagonist has granted you 
a Disjunctive Proposition, you can, using this as a 
Major Premiss, extract from him four different Con- 
clusions, if you can get him also to admit the requisite 
Minors. The Mode of two of these is technically 
called Modus Ponendo ToUens, the mode that denies 
the one alternative by granting the other — A is B, 
therefore C is not D ; C is D, therefore A is not B. 
The other Mode is also twice open, the Modus 
Tollendo Ponens— A is not B, therefore C is D ; C is 
not D, therefore A is B. 

Fallacy is sometimes committed through the Dis- 
junctive form owing to the fact that in common speech 
there is a tendency to use it in place of a mere 

^ Some logicians prefer the form Either A is, or B is. But the 
two alternatives are propositions, and if ** A is " represents a pro- 
position, the " is " is not the Syllogistic copula. If this is 
understood it does not matter: the analysis of the alternative 
propositions is unessentiaL 



i99 JWi? Interdependence of Propositions. 

hypothetical, when there are not really two incom- 
patible alternatives. Thus it may be said " Either the 
witness is perjured, or the prisoner is guilty," when the 
meaning merely is that if the witness is not perjured 
the prisoner is guilty. But really there is not a valid 
disjunction and a correct use of the disjunctive form, 
unless four hypothetical are implied, that is, unless 
the concession of either involves the denial of the 
other, and the denial of either the concession of the 
other. Now the prisoner may be guilty and yet the 
witness be perjured ; so that two of the four hypo- 
theticals, namely — 

If t4ie witness is perjured, the prisoner is not guilty. 

If the prisoner is guilty, the witness is not perjured — 
do not necessarily hold. If, then, we would guard 
against fallacy, we must always make sure before 
assenting to a disjunctive proposition that there is 
really a complete disjunction or mutual incompatibility 
between the alternatives. 



III. — The Dilemma. 

A Dilemma is a combination of Hypothetical and 
Disjunctive propositions. 

The word has passed into common speech, and its 
ordinary use is a clue to the logical structure. We are 
said to be in a dilemma when we have only two courses 
open to us and both of them are attended by unpleasant 
consequences. In argument we are in this position 
when we are shut into a choice between two admis- 
sions, and either admission leads to a conclusion which 
we do not like. The statement of the alternatives as 
the consequences hypothetically of certain conditions 
is the major premiss of the dilemma : once we admit 



Conditional Arguments. 223 

that the relations of Antecedent and Consequent are 
as stated, we are in a trap, if trap it is : we are on the 
horns of the dilemma, ready to be tossed from one to 
the other. 

For example : — 

If A is B, A is C, and if A is not B, A is D. But A 
either is or is not B. Therefore, A either is C or is D. 

If A acted of his own motive, he is a knave ; if A 
did not act of his own motive, he is a catspaw. But 
A either acted of his own motive or he did not. 
Thereupon A is either a knave or a catspaw. 

This is an example of the Constructive Dilemma, the 
iorm of it corresponding to the common use of the 
ivord as a choice between equally unpleasant alterna- 
tives. The standard example is the dilemma in which 
the custodians of the Alexandrian Library are said to 
have been put by the Caliph Omar in 640 a.d. 

If your books are in conformity with the Koran, they 
are superfluous ; if they are at variance with it, they 
are pernicious. But they must either be in conformity 
with the Koran or at variance with it. Therefore 
they are either superfluous or pernicious. 

Where caution has to be exercised is in accepting 
the clauses of the Major. We must make sure that 
the asserted relations of Reason and Consequent really 
hold. It is there that fallacy is apt to creep in and 
hide its head. The Alexandrian Librarians were rash 
in accepting the first clause of the conqueror's Major : 
it does not follow that the books are superfluous unless 
the doctrines of the Koran are not merely sound but 
contain all that is worth knowing. The propounder 
of the dilemma covertly assumes this. It is in the 
facility that it affords for what is technically known as 



224 ^^ Interdependence of Propositions. 

Petitio Principii that the Dilemma is a useful instru- 
ment for the Sophist We shall illustrate it further 
under that head. 

What is known as the Destructive Dilemma is of a 
somewhat different form. It proceeds upon the denial 
of the Consequent as involving the denial of the 
Antecedent. In the Major you obtain the admission 
that if a certain thing holds, it must be followed by one 
or other of two consequences. You then prove by way 
of Minor that neither of the alternatives is true. The 
conclusion is that the antecedent is false. 

We had an example of this in discussing whether 
the inference in the Hypothetical Syllogism is Im- 
mediate. Our argument was in this form : — 

If the inference is immediate, it must be drawn 
either from the Major alone or from the Minor alone. 
But it cannot be drawn from the Major alone, neither 
can it be drawn from the Minor alone. Therefore, it is 
not immediate. 

In this form of Dilemma, which is often serviceable 
for clearness of exposition, we must as in the other 
make sure of the truth of the Major : we must take 
care that the alternatives are really the only two 
open. Otherwise the imposing form of the argument 
is a convenient mask for sophistry. Zeno's famous 
dilemma, directed to prove that motion is impossible, 
covers 2^ petitio principii. 

If a body moves, it must move either where it is or 
where it is not. But a body cannot move where it 
is : neither can it move where it is not. Conclu- 
sion, it cannot move at all, i.^.. Motion is impossible. 

The conclusion is irresistible if we admit the Major, 
because the Major covertly assumes the point to be 



Conditional Arguments. 225 

proved. In truth, // a body moves, it moves neither 
where it is nor where it is not, but from where it is to 
where it is not. Motion consists in change of place : 
the Major assumes that the place is unchanged, that is, 
that there is no motioa. 



IS 



Chapter VIII. 

FALLACIES IN DEDUCTIVE ARGUMENT.— PETITIO 
PRINCIPII AND IGNORATIO ELENCHI. 

The traditional treatment of Fallacies in Logic follows 
Aristotle's special treatise XIcpi <ro<^toTtKa)v iXiyxo^v- 
Concerning Sophistical Refutations — Pretended Dis- 
proofs — Argumentative Tricks. 

Regarding Logic as in the main a protection against 
Fallacies, I have been going on the plan of taking each 
fallacy in connexion with its special safeguard, and in 
accordance with that plan propose to deal here with 
the two great types of fallacy in deductive argument. 
Both of them were recognised and named by Aristotle : 
but before explaining them it is worth while to indicate 
Aristotle's plan as a whole. Some of his Argumenta- 
tive Tricks were really peculiar to Yes-and-No Dialectic 
in its most sportive forms : but his leading types, both 
Inductive and Deductive, are permanent, and his plan 
as a whole has historical interest. Young readers 
would miss them from Logic: they appeal to the 
average argumentative boy. 

He divides Fallacies broadly into Verbal Fallacies 
(TrapoL rrjv Xe^iv, in dictione)^ and Non- Verbal Fallacies 
(€^0) T^s X€^€(09, extra dictionem). 

The first class are mere Verbal Quibbles, and hardly 
deserve serious treatment, still less minute sub- 
division. The world was young when time was spent 

(226^ 



Fallacies in Deductive Argument 227 

upon them, Aristotle names six varieties, but they 
all turn on ambiguity of word or structure, and some 
of them, being dependent on Greek syntax, cannot 
easily be paralleled in another tongue. 

(i) Ambiguity of word (o/iww/ua). As if one were 
to argue : " All cold can be expelled by heat : John's 
illness is a cold : therefore it can be expelled by heat ". 
Or : ^' Some afflictions are cheering, for afflictions are 
sometimes light, and light is always cheering ". The 
serious confusion of ambiguous words is met by 
Definition, as explained at length in pt ii. c. i. 

{2) Ambiguity af structure {dfi<l>i^oXia). 

"What he was beaten with was what I saw him 
beaten with : what I saw him beaten with was my 
eye : therefore, what he was beaten with was my eye." 

"How do you do?" "Do? Do what?" "I mean, 
how do you feel ? " " How do I feel ? With my 
fingers, of course; but I can see very well." "No, 
no ; I mean, how do you find yourself? " " Then why 
did you not say so ? I never exactly noticed, but I 
will tell you next time I lose myself." 

(3) Illicit conjunction (crvi/^€<ns). 

Socrates is good. Socrates is a musician. There- 
fore Socrates is a good musician. 

(4) Illicit disjunction (8tat/o€<ns). 

Socrates is a good musician. Therefore he is a good 
man. 

(5) Ambiguity of pronunciation (Trpoo-wSta, fallacia 

accentus). 
Analogies to words that differ only in accent, such 
as ov and ov, may be found in differences of pronuncia- 
tion. " Hair very thick, sir," said a barber to a 
customer, whose hair was bushy, but beginning to turn 
grey. " Yes, I daresay. But I would rather have it 



2a8 The Interdependence of Fropositions. 

thick than thin." " Ah, too thick to-day, sir." " But 
I don't want to dye it." " Excuse me, sir, I mean the 
hair of the hatmosphere, t-o-d-a-y, to-day." 

" He said, saddle me the ass. And they saddled 
himr 

(6) Ambiguity of inflexion {<rxif^<^ ^s Xcfccas, Figura 
dictionis). 

This is not easy to make intelligible in English. 
The idea is that a termination may be ambiguously 
interpreted, a neuter participle, e.g.^ taken for an active. 
Thus: "George is ailing". "Doing what, did you 
say ? Ailing ? What is he ailing ? Ginger-aleing ? " 

Non-Verbal Fallacies, or Fallacies in thought, are 
a more important division. Aristotle distinguishes 
seven. 

Of these, three are comparatively unimportant and 
trifling. One of them, known to the Schoolmen as 
Fallacia Flurium Interrogationum, was peculiar to 
Interrogative disputation. It is the trick of putting 
more than one question as one, so that a simple Yes 
commits the respondent to something implied. " Have 
you left off beating your father ? " If you answer Yes, 
that implies that you have been in the habit of beating 
him. " Has the practice of excessive drinking ceased 
in your part of the country ? " Such questions were 
unfair when the Respondent could answer only Yes 
or No The modern disputant who demands a plain 
answer Yes or No, is sometimes guilty of this trick. 

Two others, the fallacies known as A dido simpliciier 
ad dictum secundum quid, and A dicto secundum quid ad 
dictum simpliciter, are as common in modern dialectic as 
they were in ancient. The trick, conscious or uncon- 
scious, consists in getting assent to a statement with a 
qualification and proceeding to argue as if it had been 



Fallacm in Deductive Argumeni. 229 

conceded without qualification, and vice versd. For 
example, it being admitted that culture is good, a 
disputant goes on to argue as if the admission applied 
to some sort of culture in special, scientific, aesthetic, 
philosophical or moral. The fallacy was also known 
as Fallacia Accidentis. Proving that the Syllogism is 
useless for a certain purpose, and then claiming to 
have proved that it is useless for any purpose is another 
example. Getting a limited admission and then 
extending it indefinitely is perhaps the more common 
of the two forms. It is common enough to deserve a 
shorter name. 

The Fallacia Consequentis, or Non-Sequttur, which 
consists specially in ignoring the possibility of a 
plurality of causes, has already been partly explained 
in connexion with the Hypothetical Syllogism, and 
will be explained further in the Logic of Induction. 

Post hoc ergo proper hoc is a purely Inductive Fallacy, 
and will be explained in connexion with the Experi- 
mental Methods. 

There remain the two typical Deductive Fallacies, 
Petitio Principii (Surreptitious Assumption) and Igno- 
ratio Elenchi (Irrelevant Argument) about which we 
must speak more at length. 

The phrase of which Petitio Principii or Begging the 
Question is a translation — to iv apxH atTcto-^ai — was 
applied by Aristotle to an argumentative trick in 
debate by Question and Answer. The trick consisted 
in taking for granted a proposition necessary to the 
refutation without having obtained the admission of it. 
Another expression for the same thing — to cv dpxS 
\afjLpdv€iv — taking the principle for granted — is more 
descriptive. 

Generally speaking, Aristotle says, Begging the 



ajo The Interdependence of Fropositions, 

Question consists in not demonstrating the theorem. 
It would be in accordance with this general description 
to extend the name to all cases of tacitly or covertly, 
unwittingly to oneself or to one's opponent, assuming 
any premiss necessary to the conclusion. It is the 
fallacy of Surreptitious Assumption, and all cases of 
Enthymematic or Elliptical argument, where the 
unexpressed links in the chain of argument are not 
fully understood, are examples of it. By contrast, the 
articulate and explicit Syllogism is an ExpositioPrincipii, 
The only remedy for covert assumptions is to force 
them into the light.* 

Ignoraiio Elenchi^ ignoring the refutation (tov 
tXcyxov ayvota), is simply arguing beside the point, dis- 
tracting the attention by irrelevant considerations. It 
often succeeds by proving some other conclusion which 
is not the one in dispute, but has a superficial resem- 
blance to it, or is more or less remotely connected with 
it. 

It is easier to explain what these fallacies consist in 
than to illustrate them convincingly. It is chiefly in 
long arguments that the mischief is done. " A Fallacy," 
says Whately, " which when stated barely in a few 
sentences would not deceive a child, may deceive half 
the world if diluted in a quarto volume." Very rarely 
is a series of propositions put before us in regular form 
and order, all bearing on a definite point. A certain 
conclusion is in dispute, not very definitely formulated 
perhaps, and a mixed host of considerations are 
tumbled out before us. If we were perfectly clear- 



^Cp. Mr. Sidgwick*8 instructive treatise on Fallacies, Inter* 
national Scientific Series, p. 199. 



Fallacies in Deductive Argumenr, 231 

headed persons, capable of protracted concentration of 
attention, incapable of bewilderment, always on the 
alert, never in a hurry, never over-excited, absolutely 
without prejudice, we should keep our attention fixed 
upon two things while listening to an argument, the 
point to be proved, and the necessary premisses. We 
should hold the point clearly in our minds, and watch 
indefatigably for the corroborating propositions. But 
none of us being capable of this, all of us being subject 
to bewilderment by a rapid whirl of statements, and all 
of us biased more or less for or against a conclusion, 
the sophist has facilities for doing two things — taking 
for granted that he has stated the required premisses 
{petitio principii), and proving to perfect demonstration 
something which is not the point in dispute, but which 
we are willing to mistake for it {ignoratio elenchi). 

It is chiefly in the heat of argument that either 
Petitio or Ignoratio succeeds. When a fallacy con- 
tinues to perplex us in cold blood, it must have in its 
favour either some deeply-rooted prejudice or some 
peculiar intricacy in the language used, or some 
abstruseness in the matter. If we are not familiar 
with the matter of the argument, and have but a vague 
hold of the words employed, we are, of course, much 
more easily imposed upon. 

The famous Sophisms of antiquity show the fascina- 
tion exercised over us by proving something, no matter 
how irrelevant. If certain steps in an argument are 
sound, we seem to be fascinated by them so that we 
cannot apply our minds to the error, just as our senses 
are fascinated by an expert juggler. We have seen 
how plausibly Zeno's argument against the possibility 
of motion hides a Petitio : the Fatalist Dilemma is 
another example of the same sort. 



2^2 The Interdependence of Propositions. 

If it is fated that you die, you will die whether you 
call in a doctor or not, and if it is fated that you will 
recover, you will recover whether you call in a doctor 
or not. But it must be fated either that you die or 
that you recover. Therefore^ you will either die or 
recover whether you call in a doctor or not. 

Here it is tacitly assumed in the Major Premiss that 
the calling in of a doctor cannot be a link in the fated 
chain of events. In the statement of both the alter- 
native conditions, it is assumed that Fate does not act 
through doctors, and the conclusion is merely a 
repetition of this assumption, a verbal proposition 
lifter an imposing show of argument. " If Fate does 
not act through doctors, you will die whether you call 
in a doctor or not." 

The fallacy in this case is probably aided by our 
veneration for the grand abstraction of Fate and the 
awful idea of Death, which absorbs our attention and 
takes it away from the artful Petitio, 

The Sophism of Achilles and the Tortoise is the 
most triumphant of examples of Ignoratio Elenchi, 

The point that the Sophism undertakes to prove is 
that Achilles can never overtake a Tortoise once it 
has a certain start : what it really proves, and proves 
indisputably, is that he cannot overtake the Tortoise 
within a certain space or time. 

For simplicity of exposition, let us assume that the 
Tortoise has lOO yards start and that Achilles runs ten 
times as fast. Then, clearly, Achilles will not come 
up with it at the end of lOO yards, for while he has run 
loo, the Tortoise has run lo ; nor at the end of no, for 
then the Tortoise has run i more ; nor at the end of 1 1 1, 
for then the Tortoise has run ^ more ; nor at the end 
of iiixj^, for then the Tortoise has gained j^ more. 



Fallacies in Deductive Argument, 233 

So while Achilles runs this y^^, the Tortoise runs 
x^; while he runs the t^Vtt^ ^^ runs y^^^. Thus 
it would seem that the Tortoise must always keep 
ahead : he can never overtake it. 

But the conclusion is only a confusion of ideas : all 
that is really proved is that Achilles will not overtake 
the Tortoise while running 

100 + 10 + I + xV + T^iy + TTnnr + tuW» e^^- 

That is, that he will not overtake it till he has com- 
pleted the sum of this series, iii|- yards. To prove 
this is an ignoratio elenchi ; what the Sophist undertakes 
to prove is that Achilles will never overtake it, and he 
really proves that Achilles passes it between the iiith 
and ii2th yards. 

The exposure of this sophism is an example also of 
the value of a technical term. All attempts to expose 
it without using the term Ignoratio Elenchi or some- 
thing equivalent to it, succeed only in bewildering the 
student. It is customary to say that the root of the 
fallacy lies in assuming that the sum of an infinite 
series is equal to infinity. This profound error may be 
implied : but if any assumption so hard to understand 
were really required, the fallacy would have little force 
with the generality. 

It has often been argued that the Syllogism involves 
?. petitio principiiy because the Major Premiss contains 
the Conclusion, and would not be true unless the 
Conclusion were true. But this is really an Ignoratio 
Elenchi. The fact adduced, that the Major Premiss 
contains the Conclusion, is indisputable ; but this does 
not prove the Syllogism guilty of Petitio. Petitio 
principii is an argumentative trick, a conscious or 
unconscious act of deception, a covert assumption, and 



234 ^^ Interdependence of Propositions, 

the Syllogism, so far from favouring this, is an expositio 
principiiy an explicit statement of premisses such that, 
if they are true, the conclusion is true. The Syllogism 
merely shows the interdependence of premisses and 
conclusion ; its only tacit assumption is the Dictum de 
Omni, 

If, indeed, an opponent challenges the truth of the 
conclusion, and you adduce premisses necessarily 
containing it as a refutation, that is an ignoratio elenchi 
unless your opponent admits those premisses. If he 
admits them and denies the conclusion, you convict 
him of inconsistency, but you do not prove the truth 
of the conclusion. Suppose a man to take up the 
position : ** I am not mortal, for I have procured the 
elixir vitce ". You do not disprove this by saying, " All 
men are mortal, and you are a man". In denying 
that he is mortal, he denies that all men are mortal. 
Whatever is sufficient evidence that he is not mortal, 
is sufficient evidence that all men are not mortal. 
Perhaps it might be said that in arguing, " All men 
are mortal, and you are a man," it is not so much 
ignoratio elenchi as petitio principii that you commit. 
But be it always remembered that you may commit 
both fallacies at once. You may both argue beside 
the point and beg the question in the course of one 
and the same argument 



Chapter IX. 

FORMAL OR ARISTOTELIAN INDUCTION.— INDUCTIVE 
ARGUMENT. 

The distinction commonly drawn between Deduction ^ 
and Induction is that Deduction is reasoning from '■ 
general to particular, and Induction reasoning from 
particular to general. 

But it is really only as modes of argumentation that i 
the two processes can be thus clearly and fixedly opposed. 
The word Induction is used in a much wider sense 
when It is the title of a treatise on the Methods of 
Scientific Investigation. It is then used to cover all 
the processes employed in man's search into the 
system of reality; and in this search deduction is 
employed as well as induction in the narrow sense. 

We may call Induction in the narrow sense Formal 
Induction or Inductive Argument, or we may simply 
call it Aristotelian Induction inasmuch as it was the 
steps of Inductive argument that Aristotle formulated, 
and for which he determined the conditions of validity. 

Let us contrast it with Deductive argument. In 
this the questioner's procedure is to procure the admis- 
sion of a general proposition with a view to forcing 
the admission of a particular conclusion which is in 
dispute. In Inductive argument, on the other hand, it i 
is a general proposition that is in dispute, and the ^ 

(«3S) 



236 The Interdependence of Propositions. 

procedure is to obtain the admission of particular cases 
with a view to forcing the admission of this general 
proposition. 

Let the question be whether All horned animals 
ruminate. You engage to make an opponent admit 
this. How do you proceed ? You ask him whether 
he admits it about the various species. Does the ox 
ruminate? The sheep? The goat? And so on. 
The bringing in of the various particulars is the induc- 
tion (cTraywy^). 

When is this inductive argument complete ? When 
is the opponent bound to admit that all horned animals 
ruminate ? Obviously, when he has admitted it about 
every one. He must admit that he has admitted it 
about every one, in other words, that the particulars 
enumerated constitute the whole, before he can be held 
bound in consistency to admit it about the whole. 

The condition of the validity of this argument is 
ultimately the same with that of Deductive argument, 
the identity for purposes of predication of a generic 
whole with the sum of its constituent parts. The 
Axiom of Inductive Argument is, What is predicated of 
every one of the parts is predicable of the whole. This is 
the simple converse of the Axiom of Deductive argu- 
ment, the Dictum de Omniy " What is predicated of the 
whole is predicable about every one of the parts*'. 
The Axiom is simply converliole because for purposes 
of predication generic whole and specific or individual 
parts taken all together are identical. 

Practically in inductive argument an opponent is 
worsted when he cannot produce an instance to the 
contrary. Suppose he admits the predicate in question 
to be true of this, that and the other, but denies that 
this, that and the other constitute the whole class in 



Formal or Aristotelian Induction, 237 

question, he is defeated in common judgment if he 
cannot instance a member of the class about which the 
predicate does not hold. Hence this mode of induction 
became technically known as Indudio per enumerationem 
simplicem ubi non teperitur insiantia contradictoria. 
When this phrase is applied to a generalisation of fact, 
Nature or Experience is put figuratively in the position 
of a Respondent unable to contradict the inquirer. 

Such in plain language is the whole doctrine of 
Inductive Argument. Aristotle's Inductive Syllogism 
is, in effect, an expression of this simple doctrine 
tortuously in terms of the Deductive Syllogism. The 
great master was so enamoured of his prime invention 
that he desired to impress its form upon everything : 
otherwise, there was no reason for expressing the process 
of Induction syllogistically. Here is his description of 
the Inductive Syllogism :~ 

" Induction, then, and the Inductive Syllogism, consists 
in syllogising one extreme with the middle through the 
other extreme. For example, if B is middle to A and C, to 
prove through C that A belongs to B." ^ 

This may be interpreted as follows : Suppose a 
general proposition is in dispute, and that you wish to 
make it good by obtaining severally the admission of 
all the particulars that it sums up. The type of a 
general proposition in Syllogistic terminology is the 
Major Premiss, All M is P. What is the type of the 
particulars that it sums up? Obviously, the Con- 
clusion, S is P. This particular is contained in the 
Major Premiss, All M is P ; its truth is accepted as 

^ lixaytnTfi] fjLcv oZv 4(rrl koI d e| iirayotyris trvKKoyifffxbs rh 5tA rov 
ertpov 86.r€pov 6.Kpov ry /uetry trvKKoyiffacrBaL • Olov €t rwv A T [xiffov 
rh B, 5tit rov T hel^ai rb A ry B virdpxov. (An. Prior., ii, 23,) 



238 The Interdependence of Propositions. 

contained in the truth of All M is P. S is one of the 
parts of the generic whole M ; one of the individuals or 
species contained in the class M. If you wish, then, 
to establish P of All M by Induction, you must estab- 
lish P of all the parts, species, or individuals contained 
in M, that is, of all possible Sj / you must make good 
that this, that and the other S is P, and also that this, 
that and the other S constitute the whole of M. 
You are then entitled to conclude that All M is P : you 
have syllogised one Extreme with the Middle through 
the other Extreme. The formal statement of these 
premisses and conclusion is the Inductive Syllogism. 

This, that and the other S is P, Major, 
This, that and the other S is all M, Minor. 
.*. All M is P, Conclusion, 

This, that and the other magnet (i.^., magnets indivi- 
dually) attract iron. 
This, that and the other magnet (*.«., the individuals 
separately admitted) are all magnets. 
.'. All magnets attract iron. 

This, that and the other S being simply convertible 
with All M, you have only to make this conversion 
and you have a syllogism in Barbara where this, that 
and the other S figures as the Middle Term. 

The practical value of this tortuous expression is not 
obvious. Mediaeval logicians shortened it into what 
was known as the Inductive Enthymeme: "This, 
that and the other, therefore all," an obvious conclu- 
sion when this, that and the other constitute all. It 
is merely an evidence of the great master's intoxication 
with his grand invention. It is a proof also that 
Aristotle really looked at Induction from the point of 
view of Interrogative Dialectic. His question was, 



Formal or Aristotelian Induction, 239 

When is a Respondent bound to admit a general 
conclusion? And his answer was, When he has 
admitted a certain number of particulars, and cannot 
deny that those particulars constitute the whole whose 
predicate is in dispute. He was not concerned 
primarily with the analysis of the steps of an inquirer 
generalising from Nature, 



BOOK 11. 

INDUCTIVE LOGIC, OR THE LOGIC OF SCIENCE. 



i6 



INTRODUCTION. 

Perhaps the simplest way of disentangling the leading 
features of the departments of Logic is to take them 
in relation to historical circumstances. These features 
are writ large, as it were, in history. If we recognise 
that all bodies of doctrine have their origin in practical 
needs, we may conceive different ages as controlled 
each by a distinctive spirit, which issues its mandate 
to the men of the age, assigning to them their distinc- 
tive work. 

The mandate issued to the age of Plato and Aristotle 
was Bring your beliefs into harmony one with another. 
The Aristotelian Logic was framed in response to this 
order : its main aim was to devise instruments for 
making clear the coherence, the concatenation, the 
mutual implication of current beliefs. 

The mandate of the Mediaeval Spirit was Bring your 
beliefs into harmony with dogma. The mediaeval logic 
was contracted from Aristotle's under this impulse. 
Induction as conceived by him was neglected, allowed 
to dwindle, almost to disappear from Logic. Greater 
prominence was given to Deduction. 

Then as Dogmatic Authority became aggressive, 
and the Church through its officials claimed to pro- 
nounce on matters outside Theology, a new spirit was 
roused, the mandate of which was, Bring your beliefs 
into harmony with facts* It was under this impulse that 



244 Inductive LogtCy or the Logic of Science. 

a body of methodical doctrine vaguely called Induction 
gradually originated. 

In dealing with the genesis of the Old Logic, we 
began with Aristotle. None can dispute his title 
to be called its founder. But who was the founder 
of the New Logic? In what circumstances did it 
originate ? 

The credit of founding Induction is usually given 
to Francis Bacon, Lord Verulam. That great man 
claimed it for himself in calling his treatise on the 
Interpretation of Nature the Novum Organum. The 
claim is generally conceded. Reid's account of the 
matter represents the current belief since Bacon's own 
time. 

"After man had laboured in the search of truth 
near two thousand years by the help of Syllogisms, 
[Lord] Bacon proposed the method of Induction as a 
more effectual engine for that purpose. His Novum 
Organum gave a new turn to the thoughts and labours 
of 'the inquisitive, more remarkable and more useful 
than that which the Organon of Aristotle had given 
before, and may be considered as a second grand era 
in the progress of human nature. . . . Most arts have 
been reduced to rules after they had been brought to a 
considerable degree of perfection by the natural saga- 
city of artists; and the rules have been drawn from 
the best examples of the art that had been before 
exhibited ; but the art of philosophical induction was 
delineated by [Lord] Bacon in a very ample manner 
before the world had seen any tolerable example 
ofit."» 

There is a radical misconception here, which, for 
reasons that I hope to make plain, imperatively needs 

^ Hamilton's Reid^ p. 7X8. 



Introduction, 245 

to be cleared up. It obscures the very essence ol 
" philosophical induction ". 

There are three ways in which movement in any 
direction may be helped forward, Exhortation, Example, 
and Precept. Exhortation : a man may exhort to 
the practice of an art and thereby give a stimulus. 
Example : he may practise the art himself, and show 
by example how a thing should be done. Precept : he 
may formulate a clear method, and so make plain how 
to do it. Let us see what was Bacon's achievement 
in each of those three ways. 

Undoubtedly Bacon's powerful eloquence and high 
political position contributed much to make the study 
of Nature fashionable. He was high in place and 
great in intellect, one of the commanding personalities 
of his time. Taking "all knowledge for his province," 
though study was really but his recreation, he sketched , 
out a plan of universal conquest with a clearness and 
confidence that made the mob eager to range them- 
selves under his leadership. He was the magnificent 
demagogue of science. There had been champions of 
" Induction '' before him, but they had been compara- 
tively obscure and tongue-tied. 

While, however, we admit to the full the great 
services of this mighty advocate in making an " Induc- 
tive" method popular, we should not forget that he 
had pioneers even in hortatory leadership. His 
happiest watchword, the Interpretation of Nature, as 
distinguished from the Interpretation of Authoritative 
Books, was not of his invention. If we read WhewelFs 
History of the Inductive Sciences^ we shall find that 
many before him had aspired to ** give a new turn to 
the labours of the inquisitive," and in particular to 
substitute inquisition for disquisition. 



246 Inductive Logic^ or the Logic of Science. 

One might compile from Whewell a long catalogue 
of eminent men before Bacon who held that the study 
of Nature was the proper work of the inquisitive : 
Leonardo da Vinci (1452-1519), one of the wonders of 
mankind for versatility, a miracle of excellence in many 
things, painter, sculptor, engineer, architect, astro- 
nomer, and physicist; Copernicus (1473-1543), the 
author of the Heliocentric theory; Telesius (1508- 
1588), a theoretical reformer, whose De Rerum Natura 
(1565) anticipated not a little of the Novum Organum ; 
Cesalpinus (1520-1603), the Botanist; Gilbert (1540- 
1603), the investigator of Magnetism. By all these 
men experiment and observation were advocated as the 
only way of really increasing knowledge. They all 
derided mere book-learning. The conception of the 
world of sense as the original MS. of which systems of 
philosophy are but copies, was a familiar image with 
them. So also was Bacon's epigrammatic retort to 
those who wish to rest on the wisdom of the ancients, 
that antiquity is the youth of the world and that we 
are the true ancients. ** We are older," said Giordano 
Bruno, "and have lived longer than our predecessors." 

This last argument, indeed, is much older than the 
sixteenth century. It was used by the Doctor 
Mirabilis of the thirteenth, the Franciscan Friar, 
Roger Bacon (1214-1292). "The later men are, the 
more enlightened they are; and wise men now are 
ignorant of much the world will some day know." The 
truth is that if you are in search of a Father for 
Inductive Philosophy, the mediaeval friar has better 
claims than his more illustrious namesake. His 
enthusiasm for the advancement of learning was not 
less nobly ambitious and far-reaching, and he was 
himself an ardent experimenter and inventor. His 



Introduction. 247 

Opus Majus — an eloquent outline of his projects for a 
new learning, addressed in 1265 to Pope Clement IV., 
through whom he offered to give to the Church the 
empire of the world as Aristotle had given it to 
Alexander — was almost incredibly bold, comprehensive 
and sagacious. Fixing upon Authority, Custom, 
Popular Opinion, and the Pride of Supposed Knowledge, 
as the four causes of human ignorance, he urged a 
direct critical study of the Scriptures, and after an 
acute illustration of the usefulness of Grammar and 
Mathematics (widely interpreted), concluded with 
Experimental Science as the great source of human 
knowledge. I have already quoted (p. 15) the Friar's 
distinction between the two modes of Knowing, 
Argument and Experience, wherein he laid down that 
it is only experience that makes us feel certain. It 
were better, he cried in his impatience, to burn Aristotle 
and make a fresh start than to accept his conclusions 
without inquiry. 

Experimental Science, the sole mistress of Specu- 
lative Science, has three great Prerogatives among 
other parts of Knowledge. First, she tests by experi- 
ment the noblest conclusions of all other sciences. 
Next, she discovers respecting the notions which other 
sciences deal with, magnificent truths to which these 
sciences can by no means attain. Her third dignity 
is that she by her own power and without respect to 
other sciences investigates the secret of Nature. 

So far, then, as Exhortation goes. King James's 
great lawyer and statesman was not in advance of 
Pope Clement's friar. Their first principle was the 
same. It is only by facts that theories can be tested. 
Man must not impose his own preconceptions 
{anticipationes mentis) on nature. Man is only the 



248 Inductive LogiCy or the Logic of Science, 

interpreter of nature. Both were also at one in holding 
that the secrets of nature could not be discovered by 
discussion, but only by observation and experiment. 

Francis Bacon, however, went beyond all his prede- 
cessors in furnishing an elaborate Method for the 
interpretation of Nature. When he protested against 
the intellect's being left to itself (intellectus sibi permissus\ 
he meant more than speculation left unchecked by 
study of the facts. He meant also that the interpreter 
must have a method. As man, he says, cannot move 
rocks by the mere strength of his hands without 
instruments, so he cannot penetrate to the secrets of 
Nature by mere strength of his intellect without 
instruments. These instruments he undertakes to 
provide in his Inductive Method or Novum Organum 
And it is important to understand precisely what his 
methods were, because it is on the ground of them that 
he is called the founder of Inductive Philosophy, and 
because this has created a misapprehension of the 
methods actually followed by men of science. 

Ingenious, penetrating, wide-ranging, happy in 
nomenclature, the Novum Organum is a wonderful 
monument of the author's subtle wit and restless 
energy; but, beyond giving a general impulse to 
testing speculative fancies by close comparison with 
facts, it did nothing for science. His method — with 
its Tables of Preliminary Muster for the Intellect 
{tabulce comparentice primes instantiarum ad intellectum, 
facts collected and methodically arranged for the intel- 
lect to work upon) ; its Elimination upon first inspection 
of obviously accidental concomitants {Rejectio sive 
Exclusiva naturarum) ; its Provisional Hypothesis 
( Vindemiatio Prima sive Interpretatio Inchoaia) ; its 
advance to a true Induction or final Interpretation by 



Introduction, 349 

examination of special instances (he enumerates 
twenty-seven, 3x3x3, Prerogativas Instantiarum^ 
trying to show the special value of each for the 
inquirer)* — was beautifully regular and imposing, but 
it was only a vain show of a method. It was rendered 
so chiefly by the end or aim that Bacon proposed for 
the inquirer. In this he was not in advance of his 
age ; on the contrary, he was probably behind Roger 
Bacon, and certainly far behind such patient and 
concentrated thinkers as Copernicus, Gilbert, and 
Galileo — no discredit to the grandeur of his intellect 
when we remember that science was only his recreation, 
the indulgence of his leisure from Law and State. 

In effect, his method came to this. Collect as many 
instances as you can of the effect to be investigated, 
and the absence of it where you would expect it, 
arrange them methodically, then put aside guesses at 
the cause which are obviously unsuitable, then draw 
up a probable explanation, then proceed to make this 
exact by further comparison with instances. It is when 
we consider what he directed the inquirer to search for 
that we see why so orderly a method was little likely 
to be fruitful. 

He starts from the principle that the ultimate 
object of all knowledge is use, practice (scimus ut opere- 
mur). We want to know how Nature produces things 
that we may produce them for ourselves, if we can. 
The inquirer's first aim, therefore, should be to find 
out how the qualities of bodies are produced, to dis- 
cover the forma or formal causes of each quality. An 



1 The Novum Organum was never completed. Of the nine 
heads of special aids to the intellect in the final interpretation he 
completed only the first, the list of Prerogative Instances. 



250 Inductive Logic^ or the Logic of Science. 

example shows what he meant by this. Gold is a 
crowd or conjugation of various qualities or "natures"; 
it is yellow, it has a certain weight, it is malleable or 
ductile to a certain degree, it is not volatile (loses 
nothing under lire), it can be melted, it is soluble. If 
we knew the forma or formal cause of each of those 
qualities, we could make gold, provided the causes 
were within our control. The first object, then, of the 
investigator of Nature is to discover such formce^ in 
order to be able to effect the transformation of bodies. 
It may be desirable also to know the Mens processus^ 
any steps not apparent to the senses by which a body 
grows from its first germs or rudiments, and the 
schematismus or ultimate inner constitution of the body. 
But the discovery of the formce of the constituent 
qualities {naturce singulce)^ heat, colour, density or 
rarity, sweetness, saltness, and so forth, is the grand 
object of the Interpreter of Nature ; and it is for this 
that Bacon prescribed his method. 

The Sylva Sylvarum^ or Natural History, a miscel- 
laneous collection of facts and fictions, observations 
and traditions, with guesses at the explanation of 
them, affords us a measure of Bacon's own advance- 
ment as an interpreter of Nature. It was a posthumous 
work, and the editor, his secretary, tells us that he 
often said that if he had considered his reputation he 
would have withheld it from the world, because it was 
not digested according to his own method : yet he 
persuaded himself that the causes therein assigned were 
far more certain than those rendered by others, " not 
for any excellence of his own wit, but in respect of his 
continual conversation with Nature and Experience," 
and mankind might stay upon them till true Axioms 
were more fully discovered. When, however, we 



Introduction, 351 

examine the causes assigned, we find that in practice 
Bacon could not carry out his own precepts : that he 
did not attempt to creep up to an explanation by slow 
and patient ascent, but jumped to the highest 
generalisations : and that his explanatory notions were 
taken not from nature, but from the ordinary traditions 
of mediaeval physical science. He deceived himself, in 
short, in thinking that he could throw aside tradition 
and start afresh from observation. 

For example. He is struck by the phenomenon 01 
bubbles on water: "It seemeth^ somewhat strange 
that the air should rise so swiftly, while it is in the 
water, and when it cometh to the top should be stayed 
by so weak a cover as that of the bubble is ". The 
swift ascent of the air he explains as a '* motion ol 
percussion," the water descending and forcing up the 
air, and not a ** motion of levity" in the air itself. 
**The cause of the enclosure of the bubble is for that 
the appetite to resist separation or discontinuance, 
which is strong in solids, is also in liquors, though 
fainter and weaker." " The same reason is of the 
roundness of the bubble, as well for the skin of 
water as for the air within. For the air likewise 
avoideth discontinuance, and therefore casteth itself 
into a round figure. And for the stop and arrest of 
the air a little while, it showeth that the air of itself 
hath little or no appetite of ascending." * These notions 
were not taken direct from the facts : they descended 
from Aristotle. He differs from Aristotle, however, 
in his explanation of the colours of birds' feathers. 
" Aristotle giveth the cause vainly " that birds are more 
in the beams of the sun than beasts. ** But that is 

^Sylva Sylvarutttf Century i, 24. 



252 Inductive Logic^ or the Logic of Sdefux. 

manifestly untrue; for cattle are more in the sun 
than birds, that live commonly in the woods or 
in some covert. The true cause is that the excremen- 
titious moisture of living creatures, which maketh as 
well the feathers in birds as the hair in beasts, passeth 
in birds through a finer and more delicate strainer 
than it doth in beasts. For feathers pass through 
quills, and hair through skin." It is an instance of 
percolation or filtering : other effects of the same cause 
being the gums of trees, which are but a fine passage or 
straining of the juice through the wood and bark, and 
Cornish Diamonds and Rock Rubies, which are in like 
manner **fine exudations of stone ".^ 

These examples of Bacon's Inductions are taken 
from the Sylva at random. But the example which 
best of all illustrates his attitude as a scientific 
investigator is the remark he makes in the Novum 
Organum about the Copernican theory. Elsewhere he 
says that there is nothing to choose between it and the 
Ptolemaic ; and in the Novum Organum (lib. ii. 5) he 
remarks that " no one can hope to terminate the 
question whether in diurnal motion it is really the 
earth or the sky that rotates, unless he shall first have 
comprehended the nature of spontaneous rotation'*. 
That is, we must first find out the forma or formal 
cause of spontaneous rotation. This is a veritable 
instantia cruets, as fixing Bacon's place in the mediaeval 
and not in the new world of scientific speculation. 

Bacon, in short, in the practice of induction did not 
advance an inch beyond Aristotle. Rather he retro- 
graded, inasmuch as he failed to draw so clear a line 
between the respective spheres of Inductive collection 

^ Sylva Sylvaruntf Century x, 5, 



Tntroduetion. 253 

of facts and Explanation. There are two sources of 
general propositions, according to Aristotle, Induction 
and Nous. By Induction he meant the generalisation 
of facts open to sense, the summation of observed 
particulars, the inductio per enumerationem simplicem of 
the schoolmen. By Nous he meant the Reason or 
Speculative Faculty, as exercised with trained sagacity 
by experts. Thus by Induction we gather that all 
horned animals ruminate. The explanation of this 
is furnished by the Nous, and the explanation that 
commended itself to the trained sagacity of his time 
was that Nature having but a limited amount of hard 
material and having spent this on the horns, had none 
left for teeth, and so provided four stomachs by way of 
compensation. Bacon's guesses at causes are on the 
same scientific level with this, only he rather confused 
matters by speaking of them as if they were inductions 
from fact, instead of being merely fancies superinduced 
upon fact. His theory of interpretation, it is true, was 
so far an advance that he insisted on the necessity of 
verifying every hypothesis by further appeal to facts, 
though in practice he himself exercised no such 
patience and never realised the conditions of verification. 
Against this, again, must be set the fact that by tailing 
his method induction, and laying so much stress on 
the collection of facts, he fostered, and, indeed, fixed 
in the public mind the erroneous idea that the whole 
work of science consists in observation. The goal of 
science, as Herschel said, is Explanation, though 
every explanation must be made to conform to fact, 
and explanation is only another term for attaining to 
higher generalisations, higher unities. 

The truth is that Induction, if that is the name we 
use for scientific method, is not, as Reid conceived, an 



254 Inductive LogiCy or the Logic of Science. 

exception to the usual rule of arts in being the idvention 
of one man. Bacon neither invented nor practised it. 
It was perfected gradually in the practice of men of 
science. The birthplace of it as a conscious method 
was in the discussions of the Royal Society of London, 
as the birthplace of the Aristotelian Logic was in the 
discussions of the Athenian schools. Its first great 
triumph was Newton's law of Gravitation. If we are 
to name it after its first illustrious practitioner, we 
must call it the Newtonian method, not the Baconian. 
Newton really stands to the Scientific Method of 
Explanation as Aristotle stands to the Method of 
Dialectic and Deduction. He partly made it explicit 
in his jRegulcB Philosophandi (1685). Locke, his friend 
and fellow-member of the Royal Society, who applied 
the method to the facts of Mind in his Essay Concerning 
Human Understanding (1691), made it still further 
explicit in the Fourth Book of that famous work. 

It was, however, a century and a half later that an 
attempt was first made to incorporate scientific method 
with Logic under the name of Induction, and add it as 
a new wing to the old Aristotelian building. This was 
the work of John Stuart Mill, whose System of Logic, 
Deductive and Inductive, was first published in 1843. 

The genesis of Mill's System of Logic, as of other 
things, throws light upon its character. And in 
inquiries into the genesis of anything that man makes 
we may profitably follow Aristotle's division of causes. 
The Efficient Cause is the man himself, but we have 
also to find out the Final Cause, his object or purpose 
in making the thing, the Material Cause, the sources 
of his material, and the Formal Cause, the reason why 
he shaped it as he did. In the case of Mill's system 
we have to ask : What first moved him to formulate 



Introduction. 255 

the methods of scientific investigatioQ ? Whence did 
he derive his materials ? Why did he give his scientific 
method the form of a supplement to the old Aristotelian 
Logic? We cannot absolutely separate the three 
inquiries, but motive, matter and form each had a 
traceable influence on the leading features of his 
System. 

First, then, as to his motive. It is a mistake to 
suppose that Mill's object was to frame an organon 
that might assist men of science as ordinarily under- 
stood in making discoveries. Bacon, his secretary 
tells us, was wont to complain that he should be 
forced to be a Workman and a Labourer in science 
when he thought he deserved to be an Architect in this 
building. And men of science have sometimes rebuked 
Mill for his presumption in that, not being himself an 
investigator in any department of exact science, he should 
volunteer to teach them their business. But Mill was 
really guilty of no such presumption. His object, on 
the contrary, was to learn their method with a view to 
its application to subjects that had not yet undergone 
scientific treatment. Briefly stated, his purpose 
was to go to the practical workers in the exact 
sciences. Astronomy, Chemistry, Heat, Light, Elec- 
tricity, Molar and Molecular Physics; ascertain, 
not so much how they made their discoveries as 
how they assured themselves and others that their 
conclusions were sound ; and having ascertained their 
tests of truth and principles of proof, to formulate these 
tests so that they might be applied to propositions 
outside the range of the exact sciences, propositions in 
Politics, Ethics, History, Psychology. More particu- 
larly he studied how scientific men verify, and when 
they accept as proved, propositions of causation, expla- 



250 Inductive JLogiCy or the Logic of Saena, 

nations of the causes of things. In effect, his survey 
of scientific method was designed to lead up to the 
Sixth Book in his System, the Logic of the Moral 
Sciences. There are multitudes of floating endoxes 
or current opinions concerning man and his concerns, 
assigning causes for the conduct and character of 
individuals and of communities. Mill showed himself 
quite aware that the same modes of investigation may 
not be practicable, and that it may not be possible, 
though men are always ready to assign causes with 
confidence, to ascertain causes with the same degree 
of certainty : but at least the conditions of exact verifi- 
cation should be the same, and it is necessary to see 
what they are in order to see how far they can be 
realised. 

That such was MilFs design in the main is apparent 
on internal evidence, and it was the internal evidence 
that first struck me. But there is external evidence aa 
well. We may first adduce some essays on the Spirit 
of the Age, published in the Examiner in 1831, essays 
which drew from Carlyle the exclamation, " Here is a 
new Mystic!" These essays have never been repul> 
lished, but they contain Mill's first public expression 
of the need for a method in social inquiries. He starts 
from the Platonic idea that no state can be stable in 
which the judgment of the wisest in political affairs is 
not supreme. He foresees danger in the prevalent 
anarchy of opinion. How is it to be averted ? How 
are men to be brought to accept loyally the judgment 
of the expert in public affairs ? They accept at once 
and without question the decisions of the specially 
skilled in the physical sciences. Why is this ? For 
one reason, because there is complete agreement 
among experts. And why is there this complete 



Introduction, i5J 

agreement? Because all accept the same tests of 
truth, the same conditions of proof. Is it not possible 
to obtain among political investigators similar 
unanimity as to their methods of arriving at con- 
clusions, so as to secure similar respect for their 
authority ? 

We need not stop to ask whether this was a vain 
dream, and whether it must not always be the case 
that to ensure confidence in a political or moral 
adviser more is needed than faith in his special know- 
ledge and trained sagacity. Our point is that in 
183 1 Mill was in search of a method of reasoning in 
social questions. Opportunely soon after, early in 
1832, was published Herschel's Discourse on the Study 
of Natural Philosophy y the first attempt by an eminent 
man of science to make the methods of science 
explicit. Mill reviewed this book in the Examiner^ 
and there returns more definitely to the quest on which 
he was bent. "The uncertainty," he says, "that 
hangs over the very elements of moral and social 
philosophy proves that the means of arriving at the 
truth in those sciences are not yet properly understood. 
And whither can mankind so advantageously turn, in 
order to learn the proper means and to form their 
minds to the proper habits, as to that branch of know- 
ledge in which by universal acknowledgment the 
greatest number of truths have been ascertained and 
the greatest possible degree of certainty arrived at ? " 

We learn from Mill himself that he made an attempt 
about this time, while his mind was full of Herschers 
Discourse, to connect a scientific method with the 
body of the Old Logic. But he could not make the 
junction to his satisfaction, and abandoned the attempt 
in despair. A little later, in 1837, upon the appearance 

^1 



258 Indudive Logic, t^ the Logic of Science, 

of WhewelPs History of the Inductive Sciences, he 
renewed it, and this time with happier results. 
Wheweirs Philosophy of the Inductive Sciences was 
published in 1840, but by that time Mill's system was 
definitely shaped. 

It was, then, to Herschel and Whewell, but 
especially to the former, that Mill owed the raw materials 
of his Inductive Method. But why did he desire to 
concatenate this with the old Logic? Probably 
because he considered that this also had its uses for 
the student of society, the political thinker. He had 
inherited a respect for the old Logic from his father. 
But it was the point at which he sought to connect the 
new material with the old, the point of junction 
between the two, that determined the form of his 
system. We find the explanation of this in the history 
of the old Logic. It so happened that Whately's 
Logic was in the ascendant, and Whately's treatment 
of Induction gives the key to MilFs. 

Towards the end of the first quarter of this century 
there was a great revival of the study of Logic at 
Oxford. The study had become mechanical, Aldrich's 
Compendium, an intelligent but exceedingly brief 
abstract of the Scholastic Logic, being the text-book 
beyond which no tutor cared to go. The man who 
seems to have given new life to the study was a tutor 
who subsequently became Bishop of Llandaff, Edward 
Copleston. The first public fruits of the revival begun 
by him was Whately's article on Logic in the Encyclo- 
pczdia Meiropolitana, published as a separate book in 
1827. Curiously enough, one of Whately's most 
active collaborators in the work was John Henry 
Newman, so that the common room of Oriel, which 
Mr. Froude describes as the centre from which 



Introduction. 259 

emanated the High Church Movement, may also be 
said to have been the centre from which emanated the 
movement that culminated in the revolution of Logic. 

The publication of Whately*s Logic made a great stir. 
It was reviewed by Mill, then a youngman of twenty-one, 
in the Westminster Review (1828), and by Hamilton, then 
forty-five years of age, in the Edinburgh (1833). There 
can be no doubt that it awakened Mill's interest in the 
subject. A society formed for the discussion of philo- 
sophical questions, and called the Speculative Society, 
met at Grote's house in 1825, and for some years 
following. Of this society young Mill was a member, 
and their continuous topic in 1827 was Logic, Whately's 
treatise being used as a sort of text-book. 

It is remarkable that Mill's review of Whately, the 
outcome of these discussions, says very little about 
Induction. At that stage Mill's chief concern seems 
to have been to uphold the usefulness of Deductive 
Logic, and he even goes so far as to scoff at its 
eighteenth century detractors and their ambition to 
supersede it with a system of Induction. The most 
striking feature of the article is the brilliant defence of 
the Syllogism as an analysis of arguments to which I 
have already referred. He does not deny that an 
Inductive Logic might be useful as a supplement, but 
apparently he had not then formed the design of supply- 
ing such a supplement. When, however, that design 
seriously entered his mind, consequent upon the felt need 
of a method for social investigations, it was Whately's 
conception of Induction that he fell back upon. His- 
torically viewed, his System of Logic was an attempt 
to connect the practical conditions of proof set forth in 
HerschePs discourse with the theoretic view of Induc- 
tion propounded in Whately' s. The tag by which he 



26o Inductive Logic^ or the Logic of Science. 

sought to attach the new material to the old system 
was the Inductive Enthymeme of the Schoolmen as 
interpreted by Whately. 

Whately's interpretation — or misinterpretation — oi 
this Enthymeme, and the conception of Induction 
underlying it, since it became Mill's ruling conception 
of Induction, and virtually the formative principle of 
his system, deserves particular attention. 

"This, that and the other horned animal, ox, sheep, 
goat, ruminate; therefore^ all horned animals ruminate." 

The traditional view of this Enthymeme I have given 
in my chapter on Formal Induction (p. 238). It is 
that a Minor Premiss is suppressed : '^ This, that 
and the other constitute the wh®le dass". This is 
the form of the Minor in Aristotle^s Inductive Syllo- 
gism. 

But, Whately argued, how do we know that this, 
that and the other— the individuals we have examined 
— constitute the whole class ? Do we not assume that 
what belongs to the individuals examined belongs to 
the whole class ? This tacit assumption, he contended, 
is really at the bottom of the Enthymeme, and its 
proper completion is to take this as the Major Premiss, 
with the enumeration of individuals as the Minor. 
Thus :— 

What belongs to the individuals examined belongs to 

the whole class. 
The property of ruminating belongs to the individuals 

examined, ox, sheep, goat, etc. 
Therefore^ it belongs to all. 

In answer to this, Hamilton repeated the traditional 
view, treating Whately's view merely as an instance of 



Introduction. six 

the prevailing ignorance of the history of Logic He 
pointed out besides that Whately's Major was the 
postulate of a different kind of inference from that 
contemplated in Aristotle's Inductive Syllogism, 
Material as distinguished from Formal inference. 
This is undeniable if we take this syllogism purely as 
an argumentative syllogism The " all " of the con- 
clusion simply covers the individuals enumerated and 
admitted to be *' all '* in the Minor Premiss. If a 
disputant admits the cases produced to be all and can 
produce none to the contrary, he is bound to admit 
the conclusion. Now the inference contemplated by 
Whately was not inference from an admission to what 
it implies, but inference from a series of observations 
to all of a like kind, observed and unobserved. 

It is not worth while discussing what historical 
justification Whately had for his view of Induction. 
It is at least arguable that the word had come to mean, 
if it did not mean with Aristotle himself, more than a 
mere summation of particulars in a general statement. 
Even Aristotle's respondent in the concession of his 
Minor admitted that the individuals enumerated con- 
stituted all in the truly general sense, not merely all 
observed but all beyond the range of observation. The 
point, however, is insignificant. What really signifies 
is that while Hamilton, after drawing the line between 
Formal Induction and Material, fell back and entrenched 
himself within that line, Mill caught up Whately's 
conception of Induction, pushed forward, and made it 
the basis of his System of Logic. 

In Mill's definition, the mere summation of particu- 
lars, Inductio per enutnerationem simplicem ubi non 
reperitur instantia contradictoria^ is Induction improperly 
so called. The only process worthy of the name is 



262 Inductive Logic^ or the Logic of Science, 

Material Induction, inference to the unobserved. Here 
only is there an advance from the known to the 
unknown, a veritable " inductive hazard '*. 

Starting then with this conception of inference to 
the unobserved as the only true inference, and with an 
empirical law — a generality extended from observed 
cases to unobserved — as the type of such inference, 
Mill saw his way to connecting a new Logic with the 
old. We must examine this junction carefully, and 
the brilliant and plausible arguments by which he 
supported it ; we shall find that, biased by this desire 
to connect the new with the old, he gave a misleading 
dialectic setting to his propositions, and, in effect, 
confused the principles of Argumentative conclusion 
on the one hand and of Scientific Observation and 
Inference on the other. The conception of Inference 
which he adopted from Whately was too narrow on 
both sides for the uses to which he put it. Be ij 
understood that in the central methods both of Syllo- 
gistic and of Science, Mill was substantially in accord 
with tradition ; it is in his mode of junction, and the 
light thereby thrown upon the ends and aims of both, 
that he is most open to criticism. 

As regards the relation between Deduction and 
Induction, Mill's chief proposition was the brilliant 
paradox that all inference is at bottom Inductive, that 
Deduction is only a partial and accidental stage in a 
process the whole of which may be called Induction. 
An opinion was abroad — fostered by the apparently 
exclusive devotion of Logic to Deduction-— that all 
inference is essentially Deductive. Not so, answered 
Mill, meeting this extreme with another : all inference 
is essentially Inductive. He arrives at this through 
the conception that Induction is a generalisation from 



Introduction. 263 

observed particulars, while Deduction is merely the 
extension of the generalisation to a new case, a new 
particular. The example that he used will make his 
meaning plain. 
Take a common Syllogism :— - 

All men are mortal. 
Socrates is a man. 
Socrates is mortal. 

" The proposition,*' Mill says, ** that Socrates is mortal 
is evidently an inference. It is got at as a conclusion 
from something else. But do we in reality conclude 
it from the proposition. All men are mortal ? " He 
answers that this cannot be, because if it is not true that 
Socrates is mortal it cannot be true that all men are 
mortal. It is clear that our belief in the mortality of 
Socrates must rest on the same ground as our belief 
in the mortality of men in general. He goes on to 
ask whence we derive our knowledge of the generaj 
truth, and answers : ** Of course from observation. 
Now all which man can observe are individual cases. 
... A general truth is but an aggregate of particular 
truths. But a general proposition is not merely a 
compendious form for recording a number of particular 
facts. ... It is also a process of inference. From 
instances which we have observed we feel warranted 
in concluding that what we have found true in those 
instances, holds in all similar ones, past, present, and 
future. We then record all that we have observed 
together with what we infer from our observations, in 
one concise expression.'' A general proposition is 
thus at once a summary of particular facts and a 
memorandum of our right to infer from them. And 
when we make a deduction we are, as it were, 



264 Inductive LogiCy or the Logic of Science, 

interpreting this memorandum. But it is upon the 
particular facts that the inference really rests, and Mill 
contends that we might if we chose infer to the 
particular conclusion at once without going through 
the form of a general inference. Thus Mill seeks to 
make good his point that all inference is essentially 
Inductive, and that it is only for convenience that the 
word Induction has been confined to the general 
induction, while the word Deduction is applied to the 
process of interpreting our memorandum. 

Clear and consecutive as this argument is, it is 
fundamentally confusing. It confuses the nature 
of Syllogistic conclusion or Deduction, and at the 
same time gives a partial and incomplete account of 
the ground of Material inference. 

The root of the first confusion lies in raising the 
question of the ground of material inference in con- 
nexion with the Syllogism. As regards the usefulness 
of the Syllogism, this is an Ignoratio Elenchi. That 
the Major and the conclusion rest upon the same ground 
as matters of belief is indisputable : but it is irrelevant. 
In so far as ** Socrates is mortal " is an inference from 
facts, it is not the conclusion of a Syllogism. This is 
implicitly and with unconscious inconsistency recog- 
nised by Mill when he represents Deduction as the 
interpretation of a memorandum. To represent 
Deduction as the interpretation of a memorandum — a 
very happy way of putting it and quite in accordance 
with Roger Bacon^s view — is really inconsistent with 
regarding Deduction as an occasional step in the 
process of Induction. If Deduction is the interpretation 
of a memorandum, it is no part of the process of 
inference from facts. The conditions of correct 
interpretation as laid down in Syllogism are one thing, 



Introduction, 265 

and the methods of correct inference from facts, the 
methods of science that he was in search of, are 
another. 

Let us emphasise this view of Deduction as the 
interpretation of a memorandum. It corresponds 
exactly with the view that I have taken in discussing 
the utility of the Syllogism. Suppose we want to 
know whether a particular conclusion is consistent 
with our memorandum, what have we to look to ? We 
have to put our memorandum into such a form that it 
is at once apparent whether or not it covers our 
particular case. The Syllogism aspires to be such a 
form. That is the end rnd aim of it. It does not 
enable us to judge whether the memorandum is a 
legitimate memorandum or not. It only makes clear 
that if the memorandum is legitimate, so is the con- 
clusion. How to make clear and consistent memoranda 
of our beliefs in words is a sufficiently complete de- 
scription of the main purpose of Deductive Logic. 

Instead, then, of trying to present Deduction and 
Induction as parts of the same process, which he was 
led to do by his desire to connect the new and the old, 
Mill ought rather, in consistency as well as in the 
interests of clear system, to have drawn a line of 
separation between the two as having really different 
ends, the conditions of correct conclusion from accepted 
generalities on the one hand, and the conditions of 
correct inference from facts on the other. Whether the 
first should be called inference at all is a question of 
naming that ought to have been considered by itself. 
We may refuse to call it inference, but we only confuse 
ourselves and others if we do not acknowledge that 
in so doing we are breaking with traditional usage. 
Perhaps the best way in the interests of clearness is to 



266 Inductive Logtc^ or tM Logic of Science. 

compromise with tradition by calling the one Formal 
Inference and the other Material Inference. 

It is with the latter that the Physical Sciences are 
mainly concerned, and it was the conditions and 
methods of its correct performance that Mill desired to 
systematise in his Inductive Logic. We have next to 
see how his statement of the grounds of Material 
Inference was affected by his connexion of Deduction 
and Induction. Here also we shall find a reason for a 
clearer separation between the two departments of 
Logic. 

In his antagonism to a supposed doctrine that all 
reasoning is from general to particular, Mill maintained 
simpliciter that all reasoning is from particulars to 
particulars. Now this is true only secundum quidy and 
although in the course of his argument Mill introduced 
the necessary qualifications, the unqualified thesis was 
confusing. It is perfectly true that we may infer — we 
can hardly be said to reason — from observed particulars 
to unobserved. We may even infer, and infer correctly, 
from a single case. The village matron, called in to 
prescribe for a neighbour's sick child, infers that what 
cured her own child will cure the neighbour's, and 
prescribes accordingly. And she may be right. But 
it is also true that she may be wrong, and that no 
fallacy is more common than reasoning from particulars 
to particulars without the requisite precautions. This 
is the moral of one of the fables of Camerarius. Two 
donkeys were travelling in the same caravan, the one 
laden with salt, the other with hay. The one laden with 
salt stumbled in crossing a stream, his panniers dipped 
in the stream, the salt melted, and his burden was 
lightened. When they came to another stream, the 
donkey that was laden with hay dipped his panniers 



Introduction, 967 

in the water, expecting a similar result. Mill's illustra- 
tions of correct inference from particulars to particulars 
were really irrelevant. What we are concerned with in 
considering the grounds of Inference, is the condition 
of correct inference, and no inference to an unobserved 
case is sound unless it is of a like kind with the 
observed case or cases on which it is founded, that 
is to say, unless we are entitled to make a general 
proposition. We need not go through the form of 
making a general proposition, but if a general proposi- 
tion for all particulars of a certain description is not 
legitimate, no more is the particular inference. Mill, 
of course, did not deny this, he was only betrayed by 
the turn of his polemic irto an unqualified form of 
statement that seemed to ignore it. 

But this was not the worst defect of MilPs attempt 
at a junction of old and new through Whately*s con- 
ception of Induction. A more serious defect was due 
to the insufficiency of this conception to represent all 
the modes of scientific inference. When a certain 
attribute has been found in a certain connexion in this, 
that, and the other, to the extent of all observed 
instances, we infer that it will be found in all, that the 
connexion that has obtained within the range of our 
actual experience has obtained beyond that range and 
will obtain in the future. Call this an observed uni- 
formity of nature : we hold ourselves justified in 
expecting that the observed uniformities of nature will 
continue. Such an observed uniformity — that All 
animals have a nervous system, that All animals die, 
that Quinine cures ague — is also called an Empirical 
Law. 

But while we are justified in extending an empirical 
law beyond the limits within which it has been 



268 Inductive Logic^ or the Logic of Science. 

observed to hold good, it is a mistake to suppose that 
the main work of science is the collection of empirical 
laws, and that the only scientific inference is the 
inference from the observed prevalence of an empirical 
law to its continuance. With science the collection of 
empirical laws is only a preliminary : ** the goal of 
science," in Herschers phrase, " is explanation *\ In 
giving such prominence to empirical laws in his theory. 
Mill confined Induction to a narrower scope than 
science ascribes to it. Science aims at reaching " the 
causes of things " : it tries to penetrate behind observed 
uniformities to the explanation of them. In fact, as long 
as a science consists only of observed uniformities, as 
long as it is in the empirical stage, it is a science only 
by courtesy. Astronomy was in this stage before the 
discovery of the Law of Gravitation. Medicine is 
merely empirical as long as its practice rests upon such 
generalisations as that Quinine cures ague, without 
knowing why. It is true that this explanation may 
consist only in the discovery of a higher or deeper uni- 
formity, a more recondite law of connexion : the point 
is that these deeper laws are not always open to 
observation, and that the method of reaching them is 
not merely observing and recording. 

In the body of his Inductive Logic, Mill gave a 
sufficient account of the Method of Explanation 
as practised in scientific inquiry. It was only his 
mode of approaching the subject that was confusing, 
and made it appear as if the proper work of science 
were merely extending observed generalities, as when 
we conclude that all men will die because all men have 
died, or that all horned animals ruminate because all 
hitherto observed have had this attribute, A minor 
source of confusion incident to the same controversy 



Introduction, 2^69 

was his refusing the title of Induction proper to a mere 
summary of particulars. He seemed thereby to cast 
a slight upon the mere summation of particulars. 
And yet, according to his theory, it was those 
particulars that were the basis of the Induction 
properly so called. That all men will die is an 
inference from the observation summed up in the 
proposition that all men have died. If we refuse 
the name of Induction to the general proposition of 
fact, what are we to call it ? The truth is that the 
reason why the word Induction is applied indifferently 
to the general proposition of fact and the general pro- 
position applicable to all time is that, once we are sure 
of the facts, the transition to the inference is so simple 
an affair that it has not been found necessary in 
practice to distinguish them by different names. 

Our criticism of Mill would itself mislead if it were 
taken to mean that the methods of science which he 
formulated are not the methods of science or that his 
system of those methods is substantially incomplete. 
His Inductive Logic as a system of scientific method 
was a great achievement in organisation, a veritable 
Novum Organum of knowledge. What kept him sub- 
stantially right was that the methods which he 
systematised were taken from the practice of men of 
science. Our criticism amounts only to this, that in 
correlating the new system with the old he went upon 
a wrong track. For more than two centuries Deduction 
had been opposed to Induction, the ars disserendi to the 
ars invmiendi. In trying to reconcile them and bring 
them under one roof. Mill drew the bonds too tight. 
In stating the tern^s of the union between the two 
partners, he did not separate their spheres of work 
with sufficient distinctness. 



270 Inductive Lcgic^ or the Logic of Science. 

Mill's theory of Deduction and Induction and the 
voluminous criticism to which in its turn it has been 
subjected have undoubtedly been of great service in 
clearing up the foundations of reasoning. But the 
moral of it is that if we are to make the methods of 
Science a part of Logic, and to name this department 
Induction, it is better to discard altogether the ques- 
tions of General and Particular which are pertinent 
to Syllogism, and to recognise the new department 
simply as being concerned with a different kind of 
inference, inference from facts to what lies beyond 
them, inference from the observed to the unobserved. 

That this is the general aim and proper work of 
Science is evident from its history. Get at the secrets 
of Nature by the study of Nature, penetrate to what 
is unknown and unexperienced by help of what is 
known and has been experienced, was the cry of the 
early reformers of Science. Thus only, in Roger 
Bacon's phrase, could certainty — assured, well grounded, 
rational belief — be reached. This doctrine, like every 
other, can be understood only by what it was intended 
to deny. The way of reaching certainty that Roger 
Bacon repudiated was argument, discussion, dialectic. 
This " concludes a question but does not make us feel 
certain, or acquiesce in the contemplation of truth that 
is not also found in Experience". Argument is not 
necessarily useless ; the proposition combated is only 
that by it alone — by discussion that does not go beyond 
accepted theories or conceptions— rational belief about 
the unknown cannot be reached. The proposition 
affirmed is that to this end the conclusions of argument 
must be tested by experience. 

Observation of facts then is a cardinal part of the 
method of Science. The facts on which our inferences 



IntroducHfm, ^ji 

are based, by which our conclusions are tested, must 
be accurate. But in thus laying emphasis on the 
necessity of accurate observation, we must beware of 
rushing to the opposite extreme, and supposing that 
observation alone is enough. Observation, the accu- 
rate use of the senses (by which we must understand 
inner as well as outer sense), is not the whole work of 
Science. We may stare at facts every minute of our 
waking day without being a whit the wiser unless we 
exert our intellects to build upon them or under them. 
To make our examination fruitful, we must have 
conceptions, theories, speculations, to bring to the test. 
The comparison of these with the facts is the inductive 
verification of them. Science has to exercise its 
ingenuity both in making hypotheses and in contriving 
occasions for testing them by observation. These 
contrived occasions are its artificial experiments, which 
have come to be called experiments simply by contrast 
with conclusive observations for which Nature herself 
furnishes the occasion. The observations of Science 
are not passive observations. The word experiment 
simply means trial, and every experiment, natural or 
artificial, is the trial of a hypothesis. In the language 
of Leonardo da Vinci, '' Theory is the general, Experi- 
ments are the soldiers ". 

Observation and Inference go hand in hand in the 
work of Science, but with a view to a methodical 
exposition of its methods, we may divide them broadly 
into Methods of Observation and Methods of Inference. 
There are errors specially incident to Observation, and 
errors specially incident to Inference. How to observe 
correctly and how to make correct inferences from our 
observations are the two objects of our study in Induc- 
tive Logic : we study the examples of Science because 



272 Inductive Logk^ or the Logic of Sctena. 

they have been successful in accomplishing those 
objects. 

That all inference to the unobserved is founded on 
facts, on the data of experience, need not be postulated. 
It is enough to say that Inductive Logic is concerned 
with inference in so far as it is founded on the data of 
experience. But inasmuch as all the data of experi- 
ence are not of equal value as bases of inference, it is 
well to begin with an analysis of them, if we wish to 
take a comprehensive survey of the various modes of 
inference and the conditions of their validity. 



1 



Chapter i. 

THE DATA OF EXPERIENCE AS GROUNDS OF 
INFERENCE OR RATIONAL BELIEF. 

If we examine any of the facts or particulars on which 
an inference to the unobserved is founded, we shall 
find that they are not isolated individuals or attributes, 
separate objects of perception or thought, but relations 
among things and their qualities, constituents, or 
ingredients. 

Take the "particular" from which Mill's village 
matron inferred, the fact on which she based her 
expectation of a cure for her neighbour's child. It is a 
relation between things. We have the first child's 
ailment, the administration of the drug, and the 
recovery, a series of events in sequence. This observed 
sequence is the fact from which she is said to infer, the 
datum of experience. She expects this sequence to 
be repeated in the case of her neighbour's child. 

Similarly we shall find that, in all cases where we 
infer, the facts are complex, are not mere isolated 
things, but relations among things — using the word 
thing in its widest sense — relations which we expect to 
find repeated, or believe to have occurred before, or to 
be occurring now beyond the range of our observation. 
These relations, which we may call coincidences or 
conjunctions, are the data of experience from which we 

18 (273) 



274 Inductive Logic^ or the Logic of Science. 



1 



start in our beliefs or inferences about the unex- 
perienced. 

The problem of Inductive Logic being to determine 
when or on what conditions such beliefs are rational, 
we may begin by distinguishing the data of coincidence 
or conjunction accordingly. There are certain coinci- 
dences that we expect to find repeated beyond the 
occasions on which we have observed them, and others 
that we do not expect to find repeated. If it is a sound 
basis of inference that we are in search of, it is evidently 
to these first, the coincidences that we are assured of 
finding again, that we must direct our study. Let us 
see whether they can be specified. 

(i) If there is no causal connexion between A and 
B, using these as symbols for the members of a 
coincidence — the objects that are presented together — 
we do not expect the coincidence to be repeated. If A 
and B are connected as cause and effect, we expect the 
effect to recur in company with the cause. We expect 
that when the cause reappears in similar circumstances, 
the effect also will reappear. 

You are hit, e,g^ by a snowball, and the blow is 
followed by a feeling of pain. The sun, we shall 
say, was shining at the moment of the impact of the 
snowball on your body. The sunshine preceded your 
feeling of pain as well as the blow. But you do not 
expect the pain to recur next time that the sun shines. 
You do expect it to recur next time you are hit by a 
snowball. 

The taking of food and a certain feeling of strength 
are causally connected. If we go without food, we are 
not surprised when faintness or weariness supervenes. 

Suppose that when our village matron administered 
her remedy to her own child, a dog stood by the 



Experience as ground sf Inference or Rational Belief. 275 

bedside and barked. The barking in that case would 
precede the cure. Now, if the matron were what we 
should call a superstitious person, and believed that 
this concomitant had a certain efficacy, that the dog's 
barking and the cure were causally connected, she 
would take the dog with her when she went to cure 
her neighbour's child. Otherwise she would not. She 
would say that the barking was an accidental, casual, 
fortuitous coincidence, and would build no expectation 
upon it. 

These illustrations may serve to remind us of the 
familiar fact that the causal nexus is at least one of 
the things that we depend on in our inferences to the 
unobserved. To a simple sequence we attach no 
importance, but a causal sequence or consequence that 
has been observed is a mainstay of inference. 

Whether the causal sequence holds or not as a 
matter of fact, we depend upon it if we believe in it as 
a matter of fact. But unless it does hold as a matter 
of fact, it is valueless as a guide to the unknown, and 
our belief is irrational. Clearly, therefore, if rational 
belief is what we aim at, it is of importance that we 
should make sure of cause and effect as matter of fact 
in the sequence of events. 

One large department of Inductive Logic, the so- 
called Experimental Methods, is designed to help us in 
thus making sure, /.^., in ascertaining causal sequence 
as a matter of fact. It is assumed that by careful 
observation of the circumstances, we can distinguish 
between mere simple sequence and causal sequence or 
consequence, and methods are recommended of ob- 
serving with the proper precautions against error. 

Observe that these methods, though called Inductive, 
are not concerned with arriving at general propositions. 



276 Inductive LogiCy or the Logic of Science. 

The principle we go upon is simply this, that if it can be 
ascertained as matter of fact that a certain thing is 
related to another as cause and effect, we may count 
upon the same relation as holding in unobserved 
Nature, on the general ground that like causes produce 
like effects in like circumstances. 

Observe, also, that I deliberately speak of the causal 
relation as a relation among phenomena. Whether 
this use of the words cause and effect is philosophically 
justifiable, is a question that will be raised and partly 
discussed later on. Here I simply follow the common 
usage, in accordance with which objects of perception, 
eg.y the administration of a drug and the recovery of 
a patient, are spoken of as cause and effect. Such 
observable sequences are causal sequences in the 
ordinary sense, and it is part of the work of Science to 
observe them. I do not deny that the true cause, of 
the cause that science aims ultimately at discovering, 
is to be found in the latent constitution or composition 
of the things concerned. Only that, as ^e shall see 
more precisely, is a cause of another description. 
Meantime, let us take the word to cover what it 
undoubtedly covers in ordinary speech, the perceptible 
antecedent of a perceptible consequent. 

Strictly speaking, as we shall find, Science has only 
one method of directly observing when events are in 
causal sequence. But there are various indirect 
methods, which shall be described in some sort of 
order. 

For the practical purposes of life, a single ascertained 
causal sequence is of little value as a basis of inference, 
because we can infer only to its repetition in identical 
circumstances. Suppose our village matron had been 
able to ascertain as a matter of fact— a feat as we shall 



Experience as ground of Inference or Rational Belief, 277 

find not to be achieved by direct observation — that the 
drug did cure her child, this knowledge by itself would 
have been practically valueless, because the only 
legitimate inference would have been that an exactly 
similar dose would have the same effect in exactly 
similar circumstances. But, as we shall find, though 
practically valueless, a single ascertained causal 
sequence is of supreme value in testing scientific 
speculations as to the underlying causes. 

(2) We have next to see whether there are any other 
rational expectations based on observed facts. We 
may lay down as a principle the following:— 

If a conjunction or coincidence has constantly been 
repeated within our experience^ we expect it to recur and 
believe that it has recurred outside our expedience. 

How far such expectations are rational, and with 
what degrees of confidence they should be entertained, 
are the questions for the Logic of Inference, but 
we may first note that we do as a matter of habit 
found expectations on repeated coincidence, and indeed 
guide our daily life in this way. If we meet a man 
repeatedly in the street at a certain hour, we go out 
expecting to meet him : it is a shock to our expectations, 
a surprise, when we do not. If we are walking along 
a road and find poles set up at regular intervals, we 
continue our walk expecting to find a pole coincident 
with the end of each interval. 

What Mill calls the uniformities of Nature, the uni- 
formities expressed in general propositions, are from 
the point of view of the observer, examples of repeated 
coincidence. Birth, growth, decay, death, are not 
isolated or variable coincidences with organised being : 
all are born, all grow, all decay, and all die. These 
uniformities constitute the order of Nature : the coinci- 



278 Inductive Logic ^ or the Logic of Science. 

dences observed are not occasional, occurring once in 
a way or only now and then ; they turn up again and 
again. Trees are among the uniformities on the 
varied face of Nature : certain relations between the 
soil and the plant, between trunk, branches, and leaves 
are common to them. For us who observe, each 
particular tree that comes under our observation is a 
repetition of the coincidence. And so with animals : 
in each we find certain tissues, certain organs, con* 
joined on an invariable plan. 

Technically these uniformities have been divided 
into uniformities of Sequence and uniformities of 
Coexistence. Thus the repeated alternation of day 
and night is a uniformity of Sequence : the invariable 
conjunction of inertia with weight is a uniformity of 
Coexistence. But the distinction is really immaterial 
to Logic. What Logic is concerned with is the obser- 
vation of the facts and the validity of any inference 
based on them : and in these respects it makes no 
difference whether the uniformity that we observe and 
found upon is one of Sequence or of Coexistence. 

It was exclusively to such inferences, inferences 
from observed facts of repeated coincidence, that Mill 
confined himself in his theory of Induction, though not 
in his exposition of the methods. These are the 
inferences for which we must postulate what he calls 
the Uniformity of Nature. Every induction, he says, 
following Whately, may be thrown into the form of a 
Syllogism, in which the principle of the Uniformity of 
Nature is the Major Premiss, standing to the inference 
in the relation in which the Major Premiss of a 
Syllogism stands to the conclusion. If we express this 
abstractly denominated principle in propositional form, 
and take it in connexion with MilPs other saying that 



Experience as ground of Inference or Rational Belief 279 

the course of Nature is not a uniformity but uniformities, 
we shall find, I think, that this postulated Major 
Premiss amounts to an assumption that the observed 
Uniformities of Nature continue. Mill's Inductive 
Syllogism thus made explicit would be something like 
this :— 

All the observed uniformities of Nature continue. 
That all men have died is an observed uniformity. 
Therefore, it continues ; i,e.y all men will die and did die 
before the beginning of record. 

There is no doubt that this is a perfectly sound 
postulate. Like all ultimate postulates it is indemon- 
strable ; Mill's derivation of it from Experience did not 
amount to a demonstration. It is simply an assump- 
tion on which we act. If any man cares to deny it, 
there is no argument that we can turn against him. 
We can only convict him of practical inconsistency, by 
showing that he acts upon this assumption himself 
every minute^ of his waking day. If we do not believe 
in the continuance of observed uniformities, why do we 
turn our eyes to the window expecting to find it in its 
accustomed order of place ? Why do we not look for 
it in another wall ? Why do we dip our pens in ink, 
and expect the application of them to white paper to 
be followed by a black mark ? 

The principle is sound, but is it our only postulate 
in inference to the unobserved, and does the continu- 
ance of empirical laws represent all that Science 
assumes in its inferences ? Mill was not satisfied 
about this question. He pointed out a difficulty which 
a mere belief in empirical continuity does not solve. 
Why do we believe more confidently in some uniformi- 
ties than in others ? Why would a reported breach of 



2^o inductive Logfc, or the Logic of Science, MML 

one be regarded with more incredulity than that of 
another ? Suppose a traveller to return from a strange 
country and report that he had met men with heads 
growing beneath their shoulders, why would this be 
pronounced more incredible than a report that he had 
seen a grey crow ? All crows hitherto observed have 
been black, and in all men hitherto observed the heads 
have been above the shoulders : if the mere continuity 
of observed uniformities is all that we go upon in our 
inferences, a breach of the one uniformity should be 
just as improbable as a breach of the other, neither 
more nor less. Mill admitted the difficulty, and 
remarked that whoever could solve it would have 
solved the problem of Induction. Now it seems to me 
that this particular difficulty may be solved, and yet 
(eave another behind. It may be solved within the 
limits of the principle of empirical — meaning by that 
observational — continuity. The uniform blackness of 
the crow is an exception within a wider uniformity : 
the colour of animals is generally variable. Hence we 
are not so much surprised at the reported appearance 
of a grey crow : it is in accordance with the more 
general law. On the other hand, the uniform position 
of the head relative to other parts of the body is a 
uniformity as wide as the animal kingdom : it is a 
coincidence repeated as often as animals have been 
repeated, and merely on the principle that uniformities 
continue, it has an absolutely uncontradicted series in 
its favour. 

But is this principle really all that we assume ? Do 
we not also assume that behind the observed fact of 
uniformity, there is a cause for it, a cause that does 
not appear on the surface of the observation, but must 
be sought outside of its range ? And do not the various 



Experience as ground of Inference or Rational Belief. 281 

degrees of confidence with which we expect a repetition 
of the coincidence, depend upon the extent of our 
knowledge of the producing causes and the mode of 
their operation ? At bottom our belief in the continu- 
ance of the observed uniformities rests on a belief in 
the continuance of the producing causes, and till we 
know what these are our belief has an inferior warrant : 
there is less reason for our confidence. 

To go back to the illustrations with which we 
started. If we have met a man every day for months 
at a certain place at a certain hour, it is reasonable to 
expect to meet him there to-morrow, even if our know- 
ledge does not go beyond the observed facts of repeated 
coincidence. But if we know also what brings him 
there, and that this cause continues, we have a stronger 
reason for our expectation. And so with the case of 
poles at regular intervals on a road. If we know why 
they are placed there, and the range of the purpose, 
we expect their recurrence more confidently within the 
limits of that purpose. This further knowledge is a 
warrant for stronger confidence, because if we know 
the producing causes, we are in a better position for 
knowing whether anything is likely to defeat the 
coincidence. A uniformity is said to be explained 
when its cause is known, and an inference from an 
explained uniformity is always more certain than an 
inference from a uniformity that is merely empirical in 
the sense of being simply observed. 

Now, the special work of Science is to explain, in 
the sense of discovering the causes at work beneath 
what lies open to observation. In so doing it follows 
a certain method, and obeys certain conditions of 
satisfactory explanation. Its explanations are infer- 
ences from facts, inasmuch as it is conformity with 



38 2 Inductive Logic^ or the Logic of Science, 

observed facts, with outward signs of underlying causal 
nexus, that is the justification of them. But they are 
not inferences from facts in the sense above described 
as empirical inference. In its explanations also 
Science postulates a principle that may be called the 
Uniformity of Nature. But this principle is not 
merely that observed uniformities continue. It may be 
expressed rather as an assumption that the underlying 
causes are uniform in their operation, that as they have 
acted beneath the recorded experiences of mankind, so 
they have acted before and will continue to act. 

The foregoing considerations indicate a plan for a 
roughly systematic arrangement of the methods of 
Induction. Seeing that all inference from the data ol 
experience presupposes causal connexion among the 
data from which we infer, all efforts at establishing 
sound bases of inference, or rational ground for expec- 
tation fall, broadly speaking, under two heads : (i^ 
Methods of ascertaining causal connexion among 
phenomena as a matter of fact, that is, Methods of 
Observation ; and (2) Methods of ascertaining what 
the causal connexion is, that is, Methods of Explanation. 

These constitute the body of Inductive Logic. But 
there is a preliminary and a pendant. Without 
raising the question of causal connexion, we are liable 
to certain errors in ascertaining in what sequence 
and with what circumstances events really occurred. 
These tendencies to error deserve to be pointed out by 
way of warning, and this I shall attempt in a separate 
chapter on observation of facts of simple sequence. 
This is preliminary to the special methods of observing 
causal sequence. Then, by way of pendant, I shall 
consider two modes of empirical inference from data in 



Experience as ground of Inference or Rational Belief* 283 

which the causal connexion has not been ascertained 
or explained — Inference from approximate generalisa- 
tions to particular cases, and Inference from Analogy. 
Most of these methods in one form or another were 
included by Mill in his system of Inductive Logic, and 
the great merit of his work was that he did include them, 
though at some sacrifice of consistency with his intro- 
ductory theory. With regard to the kind of empirical 
inference which that theory, following the lead of 
Whately, took as the type of all inference, Logic has 
really little to say. It was this probably that was in 
MilPs mind when he said that there is no Logic of 
Observation, ignoring the fact that the Experimental 
Methods are really methods of observation, as well as 
the Methods of Eliminating Chance by calculation of 
Probability. There is no method of observing uni- 
formities except simply observing them. Nor indeed 
is there any " method " of inferring from them : we 
can only point out that in every particular inference 
from them we assume or postulate their continuance 
generally. As regards their observation, we may point 
out further that a special fallacy is incident to it, the 
fallacy of ignoring exceptions. If we arc prepossessed 
or prejudiced in favour of a uniformity, we are apt to 
observe only the favourable instances, and to be blind 
to cases where the supposed invariable coincidence 
does not occur. Thus, as Bacon remarked among his 
Idola^ we are apt to remember when our dreams come 
true, and to forget when they do not. Suppose we 
take up the notion that a new moon on a Saturday is 
invariably followed by twenty days of unsettled 
weather, one or two or a few cases in which this notably 
holds good are apt to be borne in mind, while cases 
where the weather is neither conspicuously good nor 



284 Inductive LogiCy or the Logic of Science. 

bad are apt to be overlooked. But when a warning 
has been given against this besetting fallacy, Logic 
has nothing further to say about empirical uniformities, 
except that we may infer from them with some degree 
of reasonable probability, and that if we want ground 
for a more certain inference we should try to explaio 
them. 



Chapter li 

ASCERTAINMENT OF SIMPLE FACTS IN THEIR ORDER. 
—PERSONAL OBSERVATION.— HEARSAY EVIDENCE 
—METHOD OF TESTING TRADITIONAL EVIDENCE. 

All beliefs as to simple matter of fact must rest 
ultimately on observation. But, of course, we believe 
many things to have happened that we have never 
seen. As Chaucer says : — 

But God forbede but men shoulde 'lieve 
Wei more thing than men han seen with eye. 
Man shall not weenen everything a lie 
But if himself it seeth or else doth. 

For the great bulk of matters of fact that we believe 
we are necessarily dependent on the observations of 
others. And if we are to apply scientific method to 
the ascertainment of this, we must know what errors 
we are liable to in our recollections of what we have 
ourselves witnessed, and what errors are apt to arise in 
the tradition of what purports to be the evidence of 
eye-witnesses. 

I. — Personal Observation. 

It is hard to convince anybody that he cannot trust 
implicitly to his memory of what he has himself seen. 

(285) 



286 Inductive Logic^ or the Logic of Science. 

We are ready enough to believe that others may be 
deceived : but not our own senses. Seeing is believing. 
It is well, however, that we should realise that all 
observation is fallible, even our own. 

Three great besetting fallacies or tendencies to error 
may be specified : — 

1. Liability to have the attention fastened on special 
incidents, and so diverted from other parts of the 
occurrence. 

2. Liability to confuse and transpose the sequence 
of events. 

3. Liability to substitute inference for fact. 

It is upon the first of these weaknesses in man as 
an observing machine that jugglers chiefly depend on 
working their marvels. Sleight of hand counts for 
much, but diverting the spectator's eyes for a good 
deal more. That is why they have music played and 
patter incessantly as they operate. Their patter is not 
purposeless : it is calculated to turn our eyes away 
from the movements of their nimble hands. 

It must be borne in mind that in any field of vision 
there are many objects, and that in any rapid succession 
of incidents much more passes before the eyes than the 
memory can retain in its exact order. It is of course 
in moments of excitement and hurry, when our obser- 
vation is distracted, that we are most subject to 
fallacious illusions of memory. Unconsciously we 
make a coherent picture of what we have seen, and 
very often it happens that the sequence of events is 
not what actually passed, but what we were prejudiced 
in favour of seeing. Hence the unlikelihood of finding 
exact agreement among the witnesses of any exciting 
occurrence, a quarrel, a railway accident, a collision at 
sea, the incidents of a battle. 



Ascertainment of Simple Facts in their Order. 287 

" It commonly happens," says Mr. Kinglake,* ** that 
incidents occurring in a battle are told by the most 
truthful bystanders with differences more or less wide." 
In the attack on the Great Redoubt in the Battle of the 
Alma, a young officer, Anstruther, rushed forward and 
planted the colours of the Royal Welsh — but where ? 
Some distinctly remembered seeing him dig the butt- 
end of the flagstaff into the parapet: others as distinctly 
remembered seeing him fall several paces before he 
reached it. Similarly with the incidents of the death of 
the Prince Imperial near the Italezi Hills in the Zulu 
War. He was out as a volunteer with a reconnoitring 
party. They had off-saddled at a kraal and were 
resting, when a band of Zulus crept up through the 
long grass, and suddenly opened fire and made a rush 
forward. Our scouts at once took horse, as a recon- 
noitring party was bound to do, and scampered off, 
but the Prince was overtaken and killed. At the 
Court- Martial which ensued, the five troopers gave 
the most conflicting accounts of particulars which an 
unskilled investigator would think could not possibly 
have been mistaken by eye-witnesses of the same event. 
One said that the Prince had given the order to mount 
before the Zulus fired : another that he gave the order 
directly after : a third was positive that he never gave 
the order at all, but that it was given after the surprise 
by the officer in command. One said that he saw the 
Prince vault into the saddle as he gave the order : 
another that his horse bolted as he laid hold of the 
saddle, and that he ran alongside trying to get up. 

The evidence before any Court of Inquiry into an 
exciting occurrence is almost certain to reveal similar 

^ The Invasion of the Crimea^ iii. 124 



288 Inductive Logic, or the Logic of Science. 

discrepancies. But what we find it hard to realise is 
that we ourselves can possibly be mistaken in what 
we have a distinct and positive recollection of having 
seen. It once happened to myself in a London street 
to see a drunken woman thrown under a cab by her 
husband. Two cabs were running along, a four- 
wheeler and a hansom : the woman staggered almost 
under the first, and was thrown under the second. As 
it happened the case never got beyond the police 
station to which the parties were conveyed after 
fierce opposition from some neighbours, who sympa- 
thised entirely with the man. The woman herself, 
when her wounds were dressed, acknowledged the 
justice of her punishment, and refused to charge her 
husband. I was all the more willing to acquiesce in 
this because I found that while I had the most distinct 
impression of having seen the four-wheeler run over the 
woman's body, and should have been obliged to sweat 
accordingly, there could be no doubt that it was really 
the hansom that had done so. This was not only the 
evidence of the neighbours, which I suspected at the time 
of being a trick, but of the cabdriver, who had stopped 
at the moment to abide the results of the accident. I 
afterwards had the curiosity to ask an eminent police 
magistrate. Sir John Bridge, whether this illusion of 
memory on my part— -which I can only account for by 
supposing that my eyes had been fixed on the sufferer 
and that I had unconsciously referred her injuries to 
the heavier vehicle— would have entirely discredited 
my testimony in his Court. His answer was that it 
would not ; that he was constantly meeting with such 
errors, and that if he found a number of witnesses of 
the same occurrence exactly agreed in every particular, 
he would suspect that they had talked the matter over 



Ascertainment of Simple Facts in their Order. 289 

and agreed upon what they were to say. This was 
the opinion of an experienced judge, a skilled critic of 
the defects of personal observation. An Old Bailey 
counsel for the defence, who is equally acquainted with 
the weakness of human memory, takes advantage of 
the fact that it is not generally understood by a Jury, 
and makes the fallacious assumption that glaring 
discrepancies are irreconcilable with the good faith of 
the witnesses who differ.^ 

II. — Tradition. — Hearsay Evidence. 

Next in value to personal observation, we must place 
the report, oral or written, of an eye-witness. This is 
the best evidence we can get if we have not witnessed 
an occurrence ourselves. Yet Courts of Law, which 
in consideration of the defects of personal observation 
require more than one witness to establish the truth, 
exclude hearsay evidence altogether in certain cases, 
and not without reason. 

^ The truth is, that we see much less than is commonly sup- 
posed. Not every impression is attended to that is made on the 
retina, and unless we do attend we cannot, properly speaking, be 
said to see. Walking across to college one day, I was startled by 
seeing on the face of a clock in my way that it was ten minutes to 
twelve, whereas I generally passed that spot about twenty minutes 
to twelve. I hurried on, fearing to be late, and on my arrival 
found myself in very good time. On my way back, passing the 
clock again, I looked up to see how much it was fast. It marked 
ten minutes to eight. It had stopped at that time. When I 
passed before I had really seen only the minute hand. The whole 
dial must have been on my retina, but I had looked at or attended 
to only what I was in doubt about, taking the hour for granted. 
I am bound to add that my business friends hint that it is only 
absorbed students that are capable of such mistakes, and that alert 
men of business are more circumspect. That can only be because 
they are more alive to the danger of error. 

19 



290 Inductive Logic^ or the Logic of Sciena, 

In hearing a report we are in the position of observers 
of a series of significant sounds, and we are subject to all 
the fallacies of observation already mentioned. In an 
aggravated degree, for words are harder to observe than 
visible things. Our attention is apt to be more listless 
than in presence of the actual events. Our minds dwell 
upon parts of the narrative to the neglect of other parts, 
and in the coherent story or description that we retain 
in our memories, sequences are apt to be altered and 
missing links supplied in accordance with what we 
were predisposed to hear. Thus hearsay evidence is 
subject to all the imperfections of the original observer, 
in addition to the still more insidious imperfections of 
the second observer. 

How quickly in the course of a few such transmissions 
hearsay loses all evidentiary value is simply illustrated 
by the game known as Russian Scandal. One of a 
company, A, writes down a short tale or sketch, and 
reads it to B. B repeats it to C, C to D, and so on. 
When it has thus gone the round of the company, the 
last hearer writes down his version, and it is compared 
with the original. With every willingness to play fair, 
the changes are generally considerable and significant. 

Sometimes it is possible to compare an oral tradition 
with a contemporary written record. In one of Mr. 
Hayward's Essays — ** The Pearls and Mock Pearls of 
History " — there are some examples of this disenchant- 
ing process. There is, for instance, a pretty story of 
an exchange of courtesies between the leaders of the 
French and English Guards at the battle of Fontenoy. 
The tradition runs that Lord Charles Hay stepped 
in front of his men and invited the French Guards 
to fire, to which M. d'Auteroche with no less 
chivalry responded : ** Monsieur, we never fire fiist ; 



Ascertainment of Simple Facts in their Order. 291 

you fire ". What really passed we learn from a letter 
from Lord Charles Hay to his mother, which happens 
to have been preserved. " I advanced before our 
regiment, and drank to the Frenchmen, and told them 
we were the English Guards, and hoped they would 
stand till we came, and not swim the Scheldt as they 
did the Maine at Dettingen." Tradition has changed 
this lively piece of buffoonery into an act of stately and 
romantic courtesy. The change was probably made 
quite unconsciously by some tenth or hundredth 
transmitter, who remembered only part of the story, 
and dressed the remainder to suit his own fancy. 

The question has been raised, For how long can oral 
tradition be trusted ? Newton was of opinion that it 
might be trusted for eighty years after the event. 
Others have named forty years. But if this means 
that we may believe a story that we find in circulation 
forty years after the alleged events, it is wildly extra- 
vagant. It does injustice to the Mythopceic Faculty 
of man. The period of time that suffices for the 
creation of a full-blown myth, must be measured by 
hours rather than by years. I will give an instance 
from my own observation, if that has not been entirely 
discredited by my previous confessions. The bazaars 
of the East are generally supposed to be the peculiar 
home of myth, hotbeds in which myths grow with the 
most amazing speed, but the locality of my myth is 
Aberdeen. In the summer of 1887 our town set up in 
one of its steeples a very fine carillon of Belgian bells. 
There was much public excitement over the event : the 
descriptions of enthusiastic promoters had prepared us 
to hear silvery music floating all over the town and 
filling the whole air. On the day fixed for the in- 
auguration, four hours after the time announced for 



292 Inductive Logtc^ or the Logic of Science. 

the first ceremonial peal, not having heard the bells, I 
was in a shop and asked if anything had happened to 
put off the ceremony. "Yes," I was told; ** there had 
been an accident ; they had not been properly hung, 
and when the wife of the Lord Provost had taken hold 
of a string to give the first pull, the whole machinery 
had come down." As a matter of fact all that had 
happened was that the sound of the bells was faint, 
barely audible a hundred yards from the belfry, and not 
at all like what had been expected. There were 
hundreds of people in the streets, and the myth had 
originated somehow among those who had not heard 
what they went out to hear. The shop where it was 
repeated circumstantially to me was in the main street, 
not more than a quarter of a mile from where the 
carillon had been played in the hearing of a large but 
disappointed crowd. I could not help reflecting that if 
I had been a mediaeval chronicler, I should have gon^ 
home and recorded the story, which continued to 
circulate for some days in spite of the newspapers : 
and two hundred years hence no historian would have 
ventured to challenge the truth of the contemporary 
evidence. 

III. — Method of Testing Traditional Evidence. 

It is obvious that the tests applied to descriptive 
testimony in Courts of Law cannot be applied to the 
assertions of History. It is a supreme canon of 
historical evidence that only the statements of con- 
temporaries can be admitted: but most even of their 
statements must rest on hearsay, and even when the 
historian professes to have been an eye-witness, the 
range of his observation is necessarily limited, and he 



Ascertainment of Simple Facts in their Order. 293 

cannot be put into the witness-box and cross-examined. 
Is there then no way of ascertaining historical fact ? 
Must we reject history as altogether unworthy of 
credit ? 

The rational conclusion only is that very few facts 
can be established by descriptive testimony such as 
would satisfy a Court of Law. Those who look for 
such ascertainment are on a wrong track, and are 
doomed to disappointment. It is told of Sir Walter 
Raleigh that when he was writing his History of the 
World, he heard from his prison in the Tower a 
quarrel outside, tried to find out the rights and the 
wrongs and the course of it, and failing to satisfy 
himself after careful inquiry, asked in despair how he 
could pretend to write the history of the world when he 
could not find out the truth about what occurred under 
his own windows. But this was really to set up an 
impossible standard of historical evidence. 

The method of testing historical evidence follows 
rather the lines of the Newtonian method of Explana- 
tion, which we shall afterwards describe. We must 
treat any historical record as being itself in the first 
place a fact to be explained. The statement at least is 
extant ; our first question is. What is the most rational 
way of accounting for it ? Can it be accounted for 
most probably by supposing the event stated to have 
really occurred with all the circumstances alleged ? Or 
is it a more probable hypothesis that it was the result 
of an illusion of memory on the part of the original 
observer, if it professes to be the record of an eye- 
witness, or on the part of some intermediate trans- 
mitter, if it is the record of a tradition ? To qualify 
ourselves to answer the latter kind of question with 
reasonable probability we must acquaint ourselves 



294 Inductive Logic ^ or the Logic of Science, 

with the various tendencies to error in personal 
observation and in tradition, and examine how far any 
of them are likely to have operated in the given case. 
We must study the operation of these tendencies 
within our experience, and apply the knowledge thus 
gained. We must learn from actual observation of 
facts what the Mythopoeic Faculty is capable of in 
the way of creation and transmutation, and what 
feats are beyond its powers, and then determine with 
as near a probability as we can how far it has been 
active in the particular case before us. 



I 



Chapter III. 

ASCERTAINMENT OF FACTS OF CAUSATION, 

I. — Post Hoc ergo Propter Hoc. 

One of the chief contributions of the Old Logic to 
Inductive Method was a name for a whole important 
class of misobservations. The fallacy entitled Post 
Hoc ergo Propter Hoc — ** After, therefore, Because of" — 
consisted in alleging mere sequence as a proof of 
consequence or causal sequence. The sophist appeals 
to experience, to observed facts : the sequence which 
he alleges has been observed. But the appeal is 
fallacious : the observation on which he relies amounts 
only to this, that the one event has followed upon the 
other. This much must be observable in all cases of 
causal sequence, but it is not enough for proof. Post 
hoc ergo propter hoc may be taken as a generic name for 
imperfect proof of causation from observed facts of 
succession. 

The standard example of the fallacy is the old 
Kentish peasant's argument that Tenterden Steeple 
was the cause of Goodwin Sands. Sir Thomas More 
(as Latimer tells the story in one of his Sermons to 
ridicule incautious inference) had been sent down into 
Kent as a commissioner to inquire into the cause of 
the silting up of Sandwich Haven. Among those who 
came to his court was the oldest inhabitant, and 

(29s) 



296 Inductive Logic^ or the Logic of Science, 

thinking that he from his great age must at least have 
seen more than anybody else, More asked him what 
he had to say as to the cause of the sands. " For- 
sooth, sir," was the greybeard's answer, " I am an old 
man : I think that Tenterden Steeple is the cause of 
Goodwin Sands. For I am an old man, and I may 
remember the building of Tenterden Steeple, and I 
may remember when there was no steeple at all there. 
And before that Tenterden Steeple was in building, 
there was no manner of speaking of any flats or sands 
that stopped the haven ; and, therefore, I think that 
Tenterden Steeple is the cause of the destroying and 
decaying of Sandwich Haven/' 

This must be taken as Latimer meant it to be, as a 
ridiculous example of a purely imbecile argument from 
observation, but the appeal to experience may have 
more show of reason and yet be equally fallacious. 
The believers in Kenelm Digby's ** Ointment of 
Honour" appealed to experience in support of its 
efficacy. The treatment was to apply the ointment, 
not to the wound, but to the sword that had inflicted 
it, to dress this carefully at regular intervals, and, 
meantime, having bound up the wound, to leave it 
alone for seven days. It was observed that many cures 
followed upon this treatment. But those who inferred 
that the cure was due to the bandaging of the sword, 
failed to observe that there was another circumstance 
that might have been instrumental, namely, the 
exclusion of the air and the leaving of the wound 
undisturbed while the natural. healing processes went 
on. And it was found upon further observation that 
binding up the wound alone answered the purpose 
equally well whether the sword was dressed or not. 

In cases where post hoc is mistaken for propter hoc^ 



Ascertainment of Facts of Causation. 297 

simple sequence for causal sequence, there is com- 
monly some bias of prejudice or custom which fixes 
observation on some one antecedent and diverts 
attention from other circumstances and from what 
may be observed to follow in other cases. In the 
minds of Digby and his followers there was probably 
a veneration for the sword as the weapon of honour, 
and a superstitious belief in some secret sympathy 
between the sword and its owner. So when the 
practice of poisoning was common, and suspicion was 
flurried by panic fear, observation was often at fault. 
Pope Clement VIII. was said to have been killed by 
the fumes of a poisoned candle which was placed in 
his bedroom. Undoubtedly candles were there, but 
those who attributed the Pope's death to them took no 
notice of the fact that a brazier of burning charcoal was 
at the same time in the apartment with no sufficient 
outlet for its fumes. Prince Eugene is said to have 
received a poisoned letter, which he suspected and im- 
mediately threw from him. To ascertain whether his 
suspicions were well founded the letter was administered 
to a dog, which, to make assurance doubly sure, was 
fortified by an antidote. The dog died, but no inquiry 
seems to have been made into the character of the 
antidote. 

Hotspur's retort to Glendower showed a sound sense 
of the true value to be attached to mere priority. 

Glendower. At my nativity 

The front of heaven was full of fiery shapes, 
Of burning cressets : and at my birth 
The frame and huge foundation of the earth 
Shaked like a coward. 
Hotspur, Why so it would have done at the same season, if 
your mother's cat had but kittened, though yourself had never 
been born. i Hen. IV., 3, i, 13. 



298 Inductive LogiCy or the Logic of Science, 

We all admit at once that the retort was just. 
What principle of sound conclusion was involved in 
it ? It is the business of Inductive Logic to make such 
principles explicit. 

Taking Post Hoc ergo Propter Hoc as a generic name 
for fallacious arguments of causation based on 
observed facts, for the fallacious proof of causation 
from experience, the question for Logic is, What more 
than mere sequence is required to prove consequence^ 
When do observations of Post Hoc warrant the con- 
clusion Propter Hoci 

II. — Meaning op ** Cause ".—Methods of Observa- 
tion. — Mill's Experimental Methods. 

The methods formulated by Mill under the name of 
Experimental Methods are methods actually practised 
by men of science with satisfactory results, and are 
perfectly sound in principle. They were, indeed, in 
substance, taken by him from the practice of the 
scientific laboratory and study as generalised by 
Herschel. In effect what Mill did waB to restate them 
and fit them into a system. But the controversies 
into which he was tempted in so doing have somewhat 
obscured their exact function in scientific inquiry. 
Hostile critics, finding that they did not serve the ends 
that he seemed to claim for them, have jumped to the 
conclusion that they are altogether illusory and serve 
no purpose at all. 

First, we must dismiss the notion, encouraged by 
Mill's general theory of Inference, that the Experi- 
mental Methods have anything special to do with the 
observation and inferential extension of uniformities 
such as that death is common to all organised beings. 



Ascertainment of Facts of Causation. 299 

One of the Methods, as we shall see, that named by 
Mill the Method of Agreement, does incidentally and 
collaterally establish empirical laws in the course of 
its observations, and this probably accounts for the 
prominence given to it in Mill's system. But this is 
not its end and aim, and the leading Method, that 
named by him the Method of Difference, establishes 
as fact only a particular case of causal coincidence. 
It is with the proof of theories of causation that 
the Experimental Methods are concerned : they are 
methods of observing with a view to such proof.* 

The next point to be made clear is that the facts of 
causation with which the Methods are concerned are 
observable facts, relations among phenomena, but that 
the causal relations or conditions of which they are 
the proof are not phenomena, in the meaning of being 
manifest to the senses, but rather noumena, inasmuch 
as they are reached by reasoning from what is mani^ 
fest. 

Take, for example, what is known as the quaquaversus 
principle in Hydrostatics, that pressure upon a liquid 
is propagated equally in all directions. We cannot 
observe this extension of pressure among the liquid 
particles directly. It cannot be traced among the 
particles by any of our senses. But we can assume 
that it is so, consider what ought to be visible if it is 
so, and then observe whether the visible facts are in 
accordance with the hypothesis. A box can be made, 
filled with water, and so fitted with pistons on top and 
bottom and on each of its four sides that they will 

1 This is implied, as I have already remarked, in the word 
Experimental. An experiment is a proof or trial ; of what ? Of a 
theory, a conjecture. 



300 Inductive Logic^ or the Logic of Science. 

indicate the amount of pressure on them from within. 
Let pressure then be applied through a hole in the top, 
and the pistons show that it has been communicated 
to them equally. The application of the pressure and 
the yielding of the pistons are observable facts, facts 
in causal sequence : what happens among the particles 
of the liquid is not observed but reasonably conjectured, 
is not phenomenal but noumenaL 

This distinction, necessary to an understanding of 
the scope of the Methods, was somewhat obscured by 
Mill in his preliminary discussion of the meaning of 
" cause ". Very rightly, though somewhat inconsistently 
with his first theory of Induction, he insists that " the 
notion of Cause being the root of the whole theory of 
Induction, it is indispensable that this idea should at the 
very outset of our inquiry be, with the utmost practicable 
degree of precision, fixed and determined ". But in this 
determination, not content with simply recognising 
that it is with phenomena that the Experimental 
Methods primarily deal, it being indeed only phenomena 
that can be the subjects of experimental management 
and observation, he starts by declaring that science 
has not to do with any causes except such as are 
phenomenal — ** when I speak of the cause of any 
phenomenon, I do not mean a cause which is not itself 
a phenomenon " — and goes on to define as the only 
correct meaning of cause ** the sum total of conditions," 
including among them conditions which are not 
phenomenal, in the sense of being directly open to 
observation. 

When Mill protested that he had regard only to 
phenomenal causes, he spoke as the partisan of a 
philosophical tradition. It would have been well if 
he had acted upon his own remark that the proper 



Ascertainment of Facts of Causation. 301 

understanding of the scientific method of investigating 
cause is independent of metaphysical analysis of what 
cause means. Curiously enough, this remark is the 
preface to an analysis of cause which has but slight 
relevance to science, and is really the continuation of 
a dispute begun by Hume. This is the key to his use 
of the word phenomenon : it must be interpreted with 
reference to this : when he spoke of causes as 
phenomenal, he opposed the word to " occult '' in some 
supposed metaphysical sense.^ And this irrelevant 
discussion, into the vortex of which he allowed himself 
to be carried, obscured the fact, elsewhere fully recog- 
nised by Mill himself, that science does attempt to get 
beyond phenomena at ultimate laws which are not 
themselves phenomena though they bind phenomena 
together. The *' colligation " of the facts, to use 
WhewelPs phrase, is not a phenomenon, but a 
noumenon. 

The truth is that a very simple analysis of " cause " 
is sufficient for the purposes of scientific inquiry. It is 
enough to make sure that causal sequence or conse- 
quence shall not be confounded with simple sequence. 
Causal sequence is simple sequence and something 
more, that something more being expressed by calling 
it causal. What we call a cause is not merely 
antecedent or prior in time to what we call its effect : 
it is so related to the effect that if it or an equivalent 
event had not happened the effect would not have 
happened. Anything in the absence of which a 

^ If we remember, as becomes apparent on exact psychological 
analysis, that things and their qualities are as much noumena and 
not, strictly speaking, phenomena as the attraction of gravity or 
the quaquaversus principle in liquid pressure, the prejudice against 
occultism is mitigated. 



302 Inductive Logic, &r the Logic of Science. 

phenomenon would not have come to pass as it did 
come to pass is a cause in the ordinary sense. We 
may describe it as an indispensable antecedent, with 
this reservation (which will be more fully understood 
afterwards), that if we speak of a general effect, such 
as death, the antecedents must be taken with corre- 
sponding generality. 

It is misleading to suggest, as Mill does, by defining 
cause as " the sum total of conditions " — a definition 
given to back up his conception of cause as phenomenal 
— that science uses the word cause in a different 
meaning from that of ordinary speech. It is quite true 
that " the cause, philosophically speaking, is the sum 
total of the conditions, positive and negative, taken 
together: the whole of the contingencies of every 
description, which being realised, the consequent 
invariably follows". But this does not imply any 
discrepancy between the scientific or philosophical 
meaning and the ordinary meaning. It is only another 
way of saying that the business of science or philosophy 
is to furnish a complete explanation of an event, an 
account of all its indispensable antecedents. The 
plain man would not refuse the name of cause to 
anything that science or philosophy could prove to 
be an indispensable antecedent, but his interest in 
explanation is more limited. It is confined to what he 
wants to know for the purpose he has in hand. Nor 
could the man of science consistently refuse the name 
of cause to what the plain man applies it to, if it really 
was something in consequence of which the event 
took place. Only his interest in explanation is 
different. The indispensable antecedents that he 
wants to know may not be the same. Science or 
philoaophy applies itself to the satisfaction of a wider 



Ascertainment of Facts of Causation, 303 

curiosity : it wants to know all the causes, the whole 
why, the sum total of conditions. To that end the 
various departments of science interest themselves in 
various species of conditions. But all understand the 
word cause in the ordinary sense. 

We must not conclude from accidental differences in 
explanation or statement of cause, dependent on the 
purpose in view, that the word Cause is used in 
different senses. In answering a question as to the 
cause of anything, we limit ourselves to what we 
suppose our interrogator to be ignorant of and desirous 
of knowing. If asked why the bells are ringing, we 
mention a royal marriage, or a victory, or a church 
meeting, or a factory dinner hour, or whatever the 
occasion may be. We do not consider it necessary to 
mention that the bells are struck by a clapper. Our 
hearer understands this without our mentioning it. 
Nor do we consider it necessary to mention the 
acoustic condition, that the vibration of the bells is 
communicated to our ears through the air, or the 
physiological condition, that the vibrations in the 
drums of our ears are conveyed by a certain mechanism 
of bone and tissue to the nerves. Our hearer may not 
care to know this, though quite prepared to admit 
that these conditions are indispensable antecedents. 
Similarly, a physiographer, in stating the cause of the 
periodical inundation of the Nile, would consider it 
enough to mention the melting of snow on the moun- 
tains in the interior of Africa, without saying anything 
of such conditions as the laws of gravity or the laws of 
liquefaction by heat, though he knows that these con- 
ditions are also indispensable. Death is explained by 
the doctor when referred to a gunshot wound, or a 
poison, or a virulent disease. The Pathologist may 



304 Inductive Logic^ or the Logic of Science, 

inquire further, and the Moral Philosopher further 
still. But all inquiries into indispensable conditions 
are inquiries into cause. And all alike have to be on 
their guard against mistaking simple sequence for 
consequence. 

To speak of the sum total of conditions, as the 
Cause in a distinctively scientific sense, is misleading 
in another direction. It rather encourages the idea 
that science investigates conditions in the lump, merely 
observing the visible relations between sets of ante- 
cedents and their consequents. Now this is the very 
thing that science must avoid in order to make progress. 
It analyses the antecedent situation, tries to separata 
the various coefficients, and finds out what they are 
capable of singly. It must recognise that some of the 
antecedents of which it is in search are not open to 
observation. It is these, indeed, for the most part 
that constitute the special subject-matter of the 
sciences in Molar as well as in Molecular Physics. 
For practical every-day purposes, it is chiefly the 
visible succession of phenomena that concerns us, and 
we are interested in the latent conditions only in as far 
as they provide safer ground for inference regarding 
such visible succession. But to reach the latent 
conditions is the main work of science. 

It is, however, only through observation of what is 
open to the senses that science can reach the under- 
lying conditions, and, therefore, to understand its 
methods we must consider generally what is open to 
observation in causal succession. What can be 
observed when phenomena follow one another as 
cause and effect, that is, when the one happens in con- 
sequence of the happening of the other ? In Hume's 
theory, which Mill formally adopted with a modifica- 



Ascertainment of Facts of Causation. 305 

tion/ there is nothing observable but the constancy or 
invariability of the connexion. When we say that 
Fire burns, there is nothing to be observed except that 
a certain sensation invariably follows upon close 
proximity to fire. But this holds good only if our 
observation is arbitrarily limited to the facts enounced 
in the expression. If this theory were sound, science 
would be confined to the observation of empirical laws. 
But that there is something wrong with it becomes 
apparent when we reflect that it has been ascertained 
beyond doubt that in many observed changes, and 
presumably in all, there is a transference of energy 
from one form to another. The paralogism really lies 
in the assumption from which Hume deduced his 
theory, namely, that every idea is a copy of some 
impression. As a matter of fact, we have ideas that 
are not copies of any one impression, but a binding 
together, colligation, or intellection of several impres- 
sions. Psychological analysis shows us that even when 
we say that things exist with certain qualities, we are 
expressing not single impressions or mental pheno- 
mena, but supposed causes and conditions of such, 
noumena in short, which connect our recollections of 
many separate impressions and expectations of more. 
The Experimental Methods proceed on the assump- 
tion that there is other outward and visible evidence 



^ The modification was that causation is not only ** invariable " 
but also "unconditional" sequence. This addition of uncon- 
ditionality as part of the meaning of cause, after defining cause 
as the sum total of the conditions, is very much like arguing in a 
circle. After all, the only point recognised in the theory as 
observable is the invariability of the sequence. But this is less 
important than the fact that in his canons of the Experimental 
Methods MiU recognised that more is observable. 

20 



3o6 Inductive LogiCy vr the Logic of Science, 

of causal connexion than invariability of sequence. In 
the leading Method it is assumed that when events 
may be observed to follow one another in a certain 
way, they are in causal sequence. If we can make 
sure that an antecedent change is the only change that 
has occurred in an antecedent situation, we have proof 
positive that any immediately subsequent change in 
the situation is a consequent, that the successive 
changes are in causal sequence. Thus when Pascal's 
barometer was carried to the top of Puy le Dome, and 
the mercury in it fell, the experimenters argued that 
the fall of the mercury was causally connected with 
the change of elevation, all the other circumstances 
remaining the same. This is the foundation of the 
so-called Method of Difference. To determine that the 
latent condition was a difference in the weight of the 
atmosphere, needed other observations, calculations 
and inferences ; but if it could be shown that the 
elevation was the only antecedent changed in a single 
instance, causal connexion was established between 
this and the phenomenon of the fall of the barometer. 

It is obvious that in coming to this conclusion we 
assume what cannot be demonstrated but must simply 
be taken as a working principle to be confirmed by its 
accordance with experience, that nothing comes into 
being without some change in the antecedent circum- 
stances. This is the assumption known as the Law of 
Causation — ex nikilo nihil fit. 

Again, certain observable facts are taken as evidence 
that there is no causal connexion. On the assumption 
that any antecedent in whose absence a phenomenon 
takes place is not causally connected with it, we set 
aside or eliminate various antecedents as fortuitous or 
non-causal. This negative principle, as we shall see, 



Ascertainment of Facts of Causatiim. 307 

is the foundation of what Mill called the Method of 
Agreement. 

Be it remarked, once for all, that before coming to 
a conclusion on the Positive Method or Method of 
Difference, we may often have to make many observa- 
tions on the Negative Method. Thus Pascal's experi- 
menters, before concluding that the change of altitude 
was the only influential change, tried the barometer in 
exposed positions and in sheltered, when the wind 
blew and when it was calm, in rain and in fog, in 
order to prove that these circumstances were indifferent. 
We must expound and illustrate the methods sepa- 
rately, but every method known to science may have 
in practice to be employed in arriving at a single 
conclusion. 



Chapter IV. 

METHODS OF OBSERVATION.— SINGLE DIFFERENCE. 

i. — The Principle of Single Difference.— 
Mill's "Canon". 

On what principle do we decide, in watching a suc- 
cession of phenomena, that they are connected as 
cause and effect, that one happened in consequence 
of the happening of another ? It may be worded as 
follows : — 

When the addition of an agent is followed by the 
appearance or its subtraction by the disappearance 
of a certain effect^ no other influential circumstance 
having been added or subtracted at the same time 
or in the meantime^ and no change having occurred 
among the original circumstances ^ that agent is a 
cause of the effect. 

On this principle we would justify our belief in the 
causal properties of common things — that fire burns, 
that food appeases hunger, that water quenches thirst, 
that a spark ignites gunpowder, that taking off a tight 
shoe relieves a pinched foot. We have observed the 
effect following when there was no other change in the 
antecedent circumstances, when the circumstance to 
which we refer it was simply added to or subtracted 
from the prior situation. 

(308) 



I 



Methods of Observation, 309 

Suppose we doubt whether a given agent is or is not 
capable of producing a certain effect in certain circum- 
stances, how do we put it to the proof? We add it 
singly or subtract it singly, taking care that everything 
else remains as before, and watch the result. If we 
wish to know whether a spoonful of sugar can sweeten 
a cup of tea, we taste the tea without the sugar, then 
add the sugar, and taste again. The isolated introduc- 
tion of the agent is the proof, the experiment. If we 
wish to know whether a pain in the foot is due to a 
tight lacing, we relax the lacing and make no other 
change : if the pain then disappears, we refer it to the 
lacing as the cause. The proof is the disappearance of 
the pain on the subtraction of the single antecedent. 

The principle on which we decide that there is causal 
connexion is the same whether we make the experi- 
mental changes ourselves or merely watch them as 
they occur — the only course open to us with the great 
forces of nature which are beyond the power of human 
manipulation. In any case we have proof of causation 
when we can make sure that there was only one 
difference in the antecedent circumstances correspond- 
ing to the difference of result. 

MilPs statement of this principle, which he calls the 
Canon of the Method of Difference, is somewhat more 
abstract, but the proof relied upon is substantially the 
sam®* 



If an instance in which the phenomenon under 
investigation occurs^ and an instance in which it 
does not occur ^ have every circumstance in common 
save one, that one occurring only in the. former, the 
circumstance in which alone the two instances differ 



3IO Inductive LogiCy or the Logic of Science. 

is [the effect f or] * the cause^ or an indispensable part 
of the cause^ of the phenomenon. 

Mill's statement has the merit of exactness, but 
besides being too abstract to be easy of application, the 
canon is apt to mislead in one respect. The wording 
of it suggests that the two instances required must be 
two separate sets of circumstances, such as may be 
put side by side and compared, one exhibiting the 
phenomenon and the other not. Now in practice it is 
commonly one set of circumstances that we observe 
with a special circumstance introduced or withdrawn : 
the two instances, the data of observation, are furnished 
by the scene before and the scene after the experimental 
interference. In the case, for example, of a man shot 
in the head and falling dead, death being the phenom- 
enon in question, the instance where it does not occur 
is the man's condition before he received the wound, 
and the instance where it does occur is his condition 
after, the single circumstance of difference being the 
wound, a difference produced by the addition or 
introduction of a new circumstance. Again, take the 
common coin and feather experiment, contrived to 
show that the resistance of the air is the cause of the 



^ Prof. Bain, who adopts Mill's Canon, silently drops the words 
within brackets. They seem to be an inadvertence. The " cir- 
cumstance/* in all the examples that Mill gives, is an antecedent 
circumstance. HerschePs statement, of which MilPs is an adap- 
tation, runs as follows : ** If we can either find produced by 
nature, or produce designedly for ourselves, two instances which 
agree exactly in all but one particular and differ in that one, its 
influence in producing the phenomenon, if it have any, must 
thereby be rtndored apparent "« 



Methods of Observation, 311 

feather's falling to the ground more slowly than the 
coin. The phenomenon under investigation is the 
retardation of the feather. When the two are dropped 
simultaneously in the receiver of an air-pump, the air 
being left in, the feather flutters to the ground after 
the coin. This is the instance where the phenomenon 
occurs. Then the air is pumped out of the receiver, 
and the coin and the feather being dropped at the 
same instant reach the ground together. This is the 
instance where the phenomenon does not occur. The 
single circumstance of difference is the presence of air 
in the former instance, a difference produced by the 
subtraction of a circumstance. 

Mill's Canon is framed so as to suit equally whether 
the significant difference is produced by addition to or 
subtraction from an existing sum of circumstances. 
But that it is misleading in so far as it suggests that the 
two instances must be separate sets of circumstances, 
is shown by the fact that it misled himself when he 
spoke of the application of the method in social 
investigations, such as the effect of Protection on 
national wealth. " In order," he says, ** to apply to 
the case the most perfect of the methods of experi- 
mental inquiry, the Method of Difference, we require 
to find two instances which tally in every particular 
except the one which is the subject of inquiry. We must 
have two nations alike in all natural advantages and 
disadvantages ; resembling each other in every quality 
physical and moral ; habits, usages, laws, and institu- 
tions, and differing only in the circumstance that the 
one has a prohibitory tariff and the other has not." It 
being impossible ever to find two such instances, he 
concluded that the Method of Difference could not be 
applied in social inquiries. But really it is not neces- 



312 Inductive LogtCy or the Logic of Science. 

sary in order to have two instances that we should 
have two different nations : the same nation before 
and after a new law or institution fulfils that require- 
ment. The real difficulty, as we shall see, is to satisfy 
the paramount condition that the two instances shall 
differ in a single circumstance. Every new enactment 
would be an experiment after the Method of Difference, 
if all circumstances but it remained the same till its 
results appeared. It is because this seldom or never 
occurs that decisive observation is difficult or impos- 
sible, and the simple method of difference has to be 
supplemented by other means. 

To introduce or remove a circumstance singly is the 
typical application of the principle ; but it may be em- 
ployed also to compare the effects of different agents, 
each added alone to exactly similar circumstances. A 
simple example is seen in Mr. Jamieson's agricultural 
experiments to determine the effects of different 
manures, such as coprolite and superphosphate, on 
the growth of crops. Care is taken to have all the 
antecedent circumstances as exactly alike as possible, 
except as regards the agency whose effects are to be 
observed. A field is chosen of uniform soil and even 
exposure and divided into plots : it is equally drained 
so as to have the same degree of moisture throughout ; 
the seed is carefully selected for the whole sowing. 
Between the sowing and the maturing of the crop all 
parts of the field are open to the same weather. Each 
plot may thus be regarded as practically composing 
the same set of conditions, and any difference in the 
product may with reasonable probability be ascribed to 
the single difference in the antecedents, the manures 
which it is desired to compare. 



Methods of Observation, 313 

11. — Application of the Principle. 

The principle of referring a phenomenon to the only 
immediately preceding change in antecedent circum- 
stances that could possibly have affected it, is so simple 
and so often employed by everybody every day, that 
at first we do not see how there can be any difficulty 
about it or any possibility of error. And once we 
understand how many difficulties there are in reaching 
exact knowledge even on this simple principle, and 
what care has to be taken, we are apt to overrate its 
value, and to imagine that it carries us further than it 
teally does. The scientific expert must know how to 
apply this principle, and a single application of it with 
the proper precautions may take him days or weeks, 
and yet all that can be made good by it may carry but 
a little way towards the knowledge of which he is in 
search. 

When the circumstances are simple and the effect 
follows at once, as when hot water scalds, or a blow 
with a stick breaks a pane of glass, there can be no 
doubt of the causal connexion so far, though plenty 
of room for further inquiry into the why. But the 
mere succession of phenomena may be obscure. We 
may introduce more than one agent without knowing 
it, and if some time elapses between the experimental 
interference and the appearance of the effect, other 
agents may come in without our knowledge. 

We must know exactly what it is that we introduce 
and all the circumstances into which we introduce it. 
We are apt to ignore the presence of antecedents that 
are really influential in the result. A man heated by 
work in the harvest field hastily swallows a glass of 
water, and drops down dead. There is no doubt that 



314 Inductive LogiCy or the Logic of Science. 

the drinking of the water was a causal antecedent, but 
the influential circumstance may not have been the 
quantity or the quality of the liquid but its temperature, 
and this was introduced into the situation as well as a 
certain amount of the liquid components. In making 
tea we put in so much tea and so much boiling water. 
But the temperature of the pot is also an influential 
circumstance in the resulting infusion. So in chemical 
experiments, where one might expect the result to 
depend only upon the proportions of the ingredients, 
it is found that the quantity is also influential, the 
degree of heat evolved entering as a factor into the 
result. Before we can apply the principle of single 
difference, we must make sure that there is really only 
a single difference between the instances that we 
bring into comparison. 

The air-pump was invented shortly before the foun- 
dation of the Royal Society, and its members made 
many experiments with this new means of isolating 
an agent and thus discovering its potentialities. For 
example, live animals were put into the receiver, and 
the air exhausted, with the result that they quickly 
died. The absence of the air being the sole difference, 
it was thus proved to be indispensable to life. But air 
is a composite agent, and when means were contrived 
of separating its components, the effects of oxygen 
alone and of carbonic acid alone were experimentally 
determined. 

A good example of the difficulty of excluding agencies 
other than those we are observing, of making sure that 
none £uch intrude, is found in the experiments that 
have been made in connexion with spontaneous 
generation. The question to be decided is whether 
life ever comes into existence without the antecedent 



Methods of Observation. 315 

presence of living germs. And the method of deter- 
mining this is to exclude all germs rigorously from a 
compound of inorganic matter, and observe whether 
life ever appears. If we could make sure in any one case 
that no germs were antecedently present, we should 
have proved that in that case at least life was 
spontaneously generated. 

The difficulty here arises from the subtlety of the 
agent under observation. The notion that maggots 
are spontaneously generated in putrid meat, was 
comparatively easy to explode. It was found that 
when flies were excluded by fine wire-gauze, the 
maggots did not appear. But in the case of micro- 
scopic organisms proof is not so easy. The germs are 
invisible, and it is difficult to make certain of their 
exclusion. A French experimenter, Pouchet, thought 
he had obtained indubitable cases of spontaneous 
generation. He took infusions of vegetable matter, 
boiled them to a pitch sufficient to destroy all germs 
of life, and hermetically sealed up the liquid in glass 
flasks. After an interval, micro-organisms appeared. 
Doubts as to the conclusion that they had been 
spontaneously generated turned upon two questions : 
whether all germs in the liquid had been destroyed by 
th*i preliminary boiling, and whether germs could have 
found access in the course of the interval before life 
appeared. At a certain stage in Pouchet*s process he 
had occasion to dip the mouths of the flasks in mercury. 
It occurred to Pasteur in repeating the experiments 
that germs might have found their way in from the 
atmospheric dust on the surface of this mercury. That 
this was so was rendered probable by his finding that 
when he carefully cleansed the surface of the mercury 
no life appeared afterwards in his flasks. 



3i6 Inductive Logic^ or the Logic of Science, 

The application of the principle in human affairs is 
rendered uncertain by the immense complication of 
the phenomena, the difficulty of experiment, and the 
special liability of our judgments to prejudice. That 
men and communities of men are influenced by cir- 
cumstances is not to be denied, and the influence of 
circumstances, if it is to be traced at all, must be 
traced through observed facts. Observation of the 
succession of phenomena must be part at least of any 
method of tracing cause and effect. We must watch 
what follows upon the addition of new agencies to a 
previously existing sum. But we can seldom or never 
get a decisive observation from one pair of instances, 
a clear case of difference of result preceded by a single 
difference in the antecedents. The simple Method of 
Experimental Addition or Subtraction is practically 
inapplicable. We can do nothing with a man analogous 
to putting him into a hermetically sealed retort. Any 
man or any community that is the subject of our 
observations must be under manifold influences. 
Each of them probably works some fraction of the 
total change observable, but how are they to be dis- 
entangled ? Consider, for example, how impossible it 
would be to prove in an individual case, on the strict 
principle of Single Difference, that Evil communica- 
tions corrupt good manners. Moral deterioration may 
be observed following upon the introduction of an evil 
companion, but how can we make sure that no other 
degrading influence has operated, and that no original 
depravity has developed itself in the interval ? Yet 
such propositions of moral causation can be proved 
from experience with reasonable probability. Only it 
must be by more extended observations than the strict 
Method of Difference takes into account. The method 



Methods of Observation, 317 

is to observe repeated coincidences between evil com- 
panionship and moral deterioration, and to account for 
this in accordance with still wider observations of the 
interaction of human personalities. 

For equally obvious reasons the simple Method of 
Difference is inapplicable to tracing cause and effect 
in communities. Every new law or repeal of an old 
law is the introduction of a new agency, but the effects 
of it are intermixed with the effects of other agencies 
that operate at the same time. Thus Professor Cairnes 
remarks, concerning the introduction of a high Protec- 
tive Tariff into the United States in 1861, that before 
its results could appear in the trade and manufacture 
of the States, there occurred (i) The great Civil War, 
attended with enormous destruction of capital ; (2) 
Consequent upon this the creation of a huge national 
debt, and a great increase of taxation ; (3) The issue 
of an inconvertible paper currency, deranging prices 
and wages ; (4) The discovery of great mineral 
resources and oil-springs; (5) A great extension of 
railway enterprise. Obviously in such circumstances 
other methods than the Method of Difference must be 
brought into play before there can be any satisfactory 
reasoning on the facts observed. Still what investi- 
gators aim at is the isolation of the results of single 
agencies. 



Chaptee ¥• 

METHODS OF OBSERVATION.— ELIMINATION.-^ 
SINGLE AGREEMENT. 

I. — The Principle of Elimination. 

The essence of what Mill calls the Method of Agree- 
ment is really the elimination* of accidental, casual, or 
fortuitous antecedents. It is a method employed when 
we are given an effect and set to work to discover the 
cause. It is from the effect that we start and work 
back. We make a preliminary analysis of the antece- 
dents ; call the roll, as it were, of all circumstances 
present before the effect appeared. Then we proceed 
to examine other instances of the same effect, and 
other instances of the occurrence of the various ante- 
cedents, and bring to bear the principle that any 
antecedent in the absence of which the effect has 
appeared or on the presence of which it has not 
appeared may be set aside as fortuitous, as being not 

1 Elimination, or setting aside as being of no concern, must not 
be confounded with the exclusion of agents practised in applying 
the Method of Difference. We use the word in its ordinary sense 
of putting outside the sphere of an argument. By a curious slip, 
Professor Bain follows Mill in applying the word sometimes to 
the process of singling out or disentangling a causal circumstance. 
This is an inadvertent departure from the ordinary usage, according 
to which elimination means discarding from consideration as being 
non-essential. 

(318) 



Methods of Observation. 319 

an indispensable antecedent. This is really the 
guiding principle of the method as a method of 
observation. 

Let the inquiry, for example, be into the cause of 
Endemic Goitre. Instances of the disease have been 
collected from the medical observations of all countries 
over many years. Why is it endemic in some localities 
and not in others ? We proceed on the assumption 
that the cause, whatever it is, must be some circum- 
stance common to all localities where it is endemic. 
If any such circumstance is obvious at once, we may 
conclude on the mere principle of repeated coincidence 
that there is causal connexion between it and the 
disease, and continue our inquiry into the nature of 
the connexion. But if no such circumstance is obvious, 
then in the course of our search for it we eliminate, as 
fortuitous, conditions that are present in some cases but 
absent in others. One of the earliest theories was that 
endemic goitre was connected with the altitude and 
configuration of the ground, some notorious centres of 
it being deeply cleft mountain valleys, with little air 
and wind and damp marshy soil. But wider observa- 
tion found it in many valleys neither narrower nor 
deeper than others that were exempt, and also in wide 
exposed valleys such as the Aar. Was it due to the 
geological formation ? This also had to be abandoned, 
for the disease is often incident within very narrow 
limits, occurring in some villages and sparing others 
though the geological formation is absolutely the same. 
Was it due to the character of the drinking-water ? 
Especially to the presence of lime or magnesia ? This 
theory was held strongly, and certain springs charac- 
terised as goitre-springs. But the springs in some 
goitre centres show not a trace of magnesia. The 



320 Inductive Logic, or the Logic of Science, 

comparative immunity of coast regions suggested that 
it might be owing to a deficiency of iodine in the 
drinking-water and the air, and many instances were 
adduced in favour of this. But further inquiries made 
out the presence of iodine in considerable quantities, 
in the air, the water, and the vegetation of districts 
where goitre was widely prevalent ; while in Cuba it is 
said that not a trace of iodine is discoverable either in 
the air or the water, and yet it is quite free from goitre. 
After a huge multiplication of instances, resulting in 
the elimination of every local condition that had been 
suggested as a possible cause, Hirsch came to the 
conclusion that the true cause must be a morbid poison, 
and that endemic goitre has to be reckoned among the 
infectious diseases.^ 

On this negative principle, that if a circumstance 
comes and goes without bringing the phenomenon in 
its train, the phenomenon is causally independent of 
it, common-sense is always at work disconnecting 
events that are occasionally coincident in time. A bird 
sings at our window, for example, and the clock ticks 
on the mantelpiece. But the clock does not begin to 
tick wh^n the bird begins to sing, nor cease to tick 
when the bird flies away. Accordingly, if the clock 
should stop at any time, and we wished to inquire into 
the cause, and anybody were to suggest that the 
stoppage of the clock was caused by the stoppage of 
a bird's song outside, we should dismiss the suggestion 
at once. We should eliminate this circumstance from 
our inquiry, on the ground that from other observations 
we knew it to be a casual or fortuitous concomitant. 



1 Hirsch's Geographical and Historical Pathology, Creighton's 
^anslation, vol. ii. pp. 121-202. 



Methods of Observation. 321 

Hotspur's retort to Glendover (p. 297) was based on 
this principle. When poetic sentiment or superstition 
rejects a verdict of common-sense or science, it is 
because it imagines a causal connexion to exist that is 
not open to observation, as in the case of the grand- 
father's clock which stopped short never to go again 
when the old man died. 



II. — The Principle of Single Agreement, 

The procedure in Mill's ** Method of Agreement** 
consists in thus eliminating fortuitous antecedents or 
concomitants till only one remains. We see the 
nature of the proof relied upon when we ask, How far 
must elimination be carried in order to attain proof of 
causal connexion ? The answer is that we must go on 
till we have eliminated all but one. We must multiply 
instances of the phenomenon, till we have settled of each 
of the antecedents except one that it is not the cause. 
We must have taken account of all the antecedents, 
and we must have found in our observations that all 
but one have been only occasionally present. 

When all the antecedents of an effect except one can he absent 
without the disappearance of the effect^ that one is causally 
connected with the effect^ due precautions being takei 
that no other circumstances have been present besides 
those taken account of. 

Mill's Canon of the Method of Agreement is sub- 
stantially identical with this : — 

When two or more instances of the phenomenon under 
investigation have only one circumstance in common, 
the circumstance in which alone all the instances 
agree is the cause (or effect) of the given pheno- 
menon. 

21 



322 Inductive LogiCy or the Logic of Science. 

Herschers statement, on which this canon is 
founded, runs as follows : " Any circumstance in 
which all the facts without exception agree, may be the 
cause in question, or if not, at least a collateral effect 
of the same cause : if there be but one such point of 
agreement, the possibility becomes a certainty ". 

All the instances examined must agree in one 
circumstance — hence the title Method of Agreement. 
But it is not in the agreement merely that the proof 
consists, but the agreement in one circumstance com- 
bined with difference in all the other circumstances, 
(vhen we are certain that every circumstance has come 
within our observation. It is the singleness of the 
agreement that constitutes the proof just as it is the 
singleness of the difference in the Method of Diffe- 
rence.^ 

It has been said that Mill's Method of Agreement 
amounts after all only to an uncontradicted Inductio 
per enumerationem simplicemy which he himself stigma- 
tised as Induction improperly so called. But this is 
not strictly correct. It is a misunderstanding probably 
caused by calling the method that of agreement simply, 
instead of calling it the Method of Single Agreement, 
so as to lay stress upon the process of elimination by 
which the singleness is established. It is true that 
in the course of our observations we do perform an 
induction by simple enumeration. In eliminating, we 

1 The bare titles Difference and Agreement, though they have 
the advantage of simplicity, are apt to puzzle beginners inasmuch 
as in the Method of Difference the agreement among the instances 
is at a maximum, and the difference at a minimum, and vice versd 
in the Method of Agreement. In both Methods it is really the 
isolation of the connexion between antecedent and sequent that 
constitutes the proof. 



Methods of Observation. J33 

at the same time generalise. That is to say, in 
multiplying instances for the elimination of non-causes, 
we necessarily at the same time multiply instances 
where the true causal antecedent, if there is only one 
possible, is present. An antecedent containing the 
true cause must always be there when the phenomenon 
appears, and thus we may establish by our eliminating 
observations a uniformity of connexion between two 
facts. 

Take, for example, Roger Bacon's inquiry into the 
cause of the colours of the rainbow. His first notion 
seems to have been to connect the phenomenon with 
the substance crystal, probably from his thinking of 
the crystal firmament then supposed to encircle the 
universe. He found the rainbow colours produced by 
the passage of light through hexagonal crystals. But 
on extending his observations, he found that the 
passage of light through other transparent mediums 
was also attended by the phenomenon. He found it 
in dewdrops, in the spray of waterfalls, in drops 
shaken from the oar in rowing. He thus eliminated 
the substance crystal, and at the same time established 
the empirical law that the passage of light through 
transparent mediums of a globular or prismatic shape 
was a causal antecedent of the rainbow colours.^ 

Ascertainment of invariable antecedents may thus 
proceed side by side with that of variable antecedents, 
the use of the elimination being simply to narrow the 
scope of the inquiry. But the proof set forth in Mill's 
Canon does not depend merely on one antecedent or 

^That rainbows in the sky are produced by the passage of light 
through minute drops in the clouds was an inference from this 
observed uniformity. 



324 Inductive Logic^ or the Logic of Science, 

concomitant being invariably present, but also on the 
assumption that all the influential circumstances have 
been within our observation. Then only can we be 
sure that the instances have only one circumstance in 
common. 

The truth is that owing to the difficulty of fulfilling 
this condition, proof of causation in accordance with 
Miirs Canon is practically all but impossible. It is 
not attained in any of the examples commonly given. 
The want of conclusiveness is disguised by the fact 
that both elimination and positive observation of mere 
agreement or uniform concomitance are useful and 
suggestive in the search for causes, though they do not 
amount to complete proof such as the Canon describes. 
Thus in the inquiry into the cause of goitre, the 
elimination serves some purpose though the result is 
purely negative. When the inquirer is satisfied that 
goitre is not originated by any directly observable local 
conditions, altitude, temperature, climate, soil, water, 
social circumstances, habits of exertion, his search is 
profitably limited. And mere frequency, much more 
constancy of concomitance, raises a presumption of 
causal connexion, and looking out for it is valuable as 
a mode of reconnoitring. The first thing that an 
inquirer naturally asks when confronted by numerous 
instances of a phenomenon is. What have they in 
common ? And if he finds that they have some one 
circumstance invariably or even frequently present, 
although he cannot prove that they have no other 
circumstance in common as the Canon of Single 
Agreement requires, the presumption of causal con- 
nexion is strong enough to furnish good ground for 
further inquiry. If an inquirer finds an illness with 
marked symptoms in a number of different households, 



Methods of Observation. 325 

and finds also that all the households get their milk 
supply from the same source, this is not conclusive 
proof of causation, but it is a sufficient presumption 
to warrant him in examining whether there is any 
virulent ingredient in the milk. 

Thus varying the circumstances so as to bring out 
a common antecedent, though it does not end in exact 
proof, may indicate causal connexion though it does 
not prove what the nature of the connexion is. Roger 
Bacon's observations indicated that the production of 
rainbow colours was connected with the passage of 
light through a transparent globe or prism. It was 
reserved for Newton to prove by other methods that 
white light was composed of rays, and that those rays 
were differently refracted in passing through the trans- 
parent medium. We have another example of how far 
mere agreement, revealed by varying the circumstances, 
carries us towards discovery of the cause, in Wells's 
investigation of the cause of dew. Comparing 
the numerous instances of dew appearing without 
visible fall of moisture. Wells found that they 
all agreed in the comparative coldness of the surface 
dewed. This was all the agreement that he established 
by observation ; he did not carry observation to the 
point of determining that there was absolutely no other 
common circumstance : when he had simply discovered 
or detected that this circumstance was common to 
dewed surfaces, he tried next to show by reasoning 
from other known facts how the coldness of the surface 
affected the aqueous vapour of the neighbouring air. 
He did not establish his Theory of Dew by the 
Method of Agreement: but the observation of an agree- 
ment or common feature in a number of instances was 
a stage in the process by which he reached his theory. 



326 Inductive Logic^ or the Logic of Science. 

IIL — Mill's "Joint Method of Agreement and 
Difference ". 

After examining a variety of instances in which an 
effect appears, and finding that they all agree in the 
antecedent presence of some one circumstance, we 
may proceed to examine instances otherwise similar 
{in pari materia^ as Prof. Fowler puts it) where the 
effect does not appear. If these all agree in the 
absence of the circumstance that is uniformly present 
with the effect, we have corroborative evidence that 
there is causal connexion between this circumstance 
and the effect. 

The principle of this method seems to have been 
suggested to Mill by Wells's investigations into Dew. 
Wells exposed a number of polished surfaces of various 
substances, and compared those in which there was a 
copious deposit of dew with those in which there was 
little or none. If he could have got two surfaces, one 
dewed and the other not, identical in every concomi- 
tant but one, he would have attained complete proof 
on the principle of Single Difference. But this being 
impracticable, he followed a course which approxi- 
mated to the method of eliminating every circumstance 
but one from instances of dew, and every circumstance 
but one in instances of no-dew. Mill sums up as 
follows the results of his experiments : " It appears 
that the instances in which much dew is deposited, 
which are very various, agree in this, and, so far as we 
are able to observe^ in this only, that they either radiate 
heat rapidly or conduct it slowly : qualities between 
which there is no other circumstance of agreement 
than that by virtue of either, the body tends to lose 
heat from the surface more rapidly than it can be 



Methods of Observation, 3^7 

restored from within. The instances, on the contrary, 
in which no dew, or but a small quantity of it, is 
formed, and which are also extremely various, agree 
{as far as we can observe) in nothing except in not having 
this same property. We seem therefore to have 
detected the characteristic difference between the sub- 
stances on which the dew is produced, and those on 
which it is not produced. And thus have been realised 
the requisitions of what we have termed the Indirect 
Method of Difference, or the Joint Method of Agree- 
ment and Difference." The Canon of this Method is 
accordingly stated by Mill as follows : — 

If two or more instances in which the phenomenon 
occurs have only one circumstance in common, 
while two or more instances in which it does not 
occur have nothing in common save the absence of 
that circumstance ; the circumstance in which alone 
the two sets of instances differ, is the effect, or the 
cause, or an indispensable part of the cause, of the 
phenomenon. 

In practice, however, this theoretical standard of 
proof is never attained. What investigators really 
proceed upon is the presumption afforded, to use Prof. 
Bain's terms, by Agreement in Presence combined 
with Agreement in Absence. When it is found that 
all substances which have a strong smell agree in 
being readily oxidisable, and that the marsh gas or 
carbonetted hydrogen which has no smell is not 
oxidisable at common temperatures, the presumption 
that oxidation is one of the causal circumstances in 
smell is strengthened, even though we have not suc- 
ceeded in eliminating every circumstance but this one 
from either the positive or the negative instances. So 
in the following examples given by Prof. Fowler there 



328 Inductive Logic ^ or the Logic of Science. 

is not really a compliance with the theoretical require* 
ments of Mill's Method : there is only an increased 
presumption from the double agreement. ** The Joint 
Method of Agreement and Difference (or the Indirect 
Method of Difference, or, as I should prefer to call it, 
the Double Method of Agreement) is being continually 
employed by us in the ordinary affairs of life. If when 
I take a particular kind of food, I find that I invari* 
ably suffer from some particular form of illness, 
whereas, when I leave it off, I cease to suffer, I enter- 
tain a double assurance that the food is the cause of 
piy illness. I have observed that a certain plant is 
invariably plentiful on a particular soil ; if, with a 
wide experience, I fail to find it growing on any other 
soil, I feel confirmed in my belief that there is in this 
particular soil some chemical constituent, or some 
peculiar combination of chemical constituents, which 
is highly favourable, if not essential, to the growth of 
the plant." 



Chapter VI. 
METHODS OF OBSERVATION.— MINOR METHODS. 

I. — Concomitant Variations. 

Whatever phenomenon varies in any manner whenever 
another phenomenon varies in some particular manner^ 
is either a cause or an effect of that phenomenon, or is 
connected with it through some fact of causation. 

This simple principle is constantly applied by us in 
connecting and disconnecting phenomena. If we hear 
a sound which waxes and wanes with the rise and fall 
of the wind, we at once connect the two phenomena. 
We may not know what the causal connexion is, but 
if they uniformly vary together, there is at once a 
presumption that the one is causally dependent on the 
other, or that both are effects of the same cause. 

This principle was employed by Wells in his 
researches into Dew. Some bodies are worse con- 
ductors of heat than others, and rough surfaces radiate 
heat more rapidly than smooth. Wells made observa- 
tions on conductors and radiators of various degrees, 
and found that the amount of dew deposited was 
greater or less according as the objects conducted heat 
slowly or radiated heat rapidly. He thus established 
what Herschel called a " scale of intensity " between 
the conducting and radiating properties of the bodies 
bedewed, and the amount of the dew deposit The 

(329) 



330 Inductive LogtCy or the Logic of Science, 

explanation was that in bad conductors the surface 
cools more quickly than in good conductors because 
heat is more slowly supplied from within. Similarly 
in rough surfaces there is a more rapid cooling because 
heat is given off more quickly. But whatever the 
explanation might be, the mere concomitant variation 
of the dew deposit with these properties showed that 
there was some causal connexion between them. 

It must be remembered that the mere fact oi con- 
comitant variation is only an index that some causal 
connexion exists. The nature of the connexion must 
be ascertained by other means, and may remain a 
problem, one of the uses of such observed facts being 
indeed to suggest problems, for inquiry. Thus a 
remarkable concomitance has been observed between 
spots on the sun, displays of Aurora Borealis, and 
magnetic storms. The probability is that they are 
causally connected, but science has not yet discovered 
how. Similarly in the various sciences properties are 
arranged in scales of intensity, and any correspondence 
between two scales becomes a subject for investigation 
on the assumption that it points to a causal connexion. 
We shall see afterwards how in social investigations 
concomitant variations in averages furnish material 
for reasoning. 

When two variants can be precisely measured, the 
ratio of their variation may be ascertained by the 
Method of Single Difference. We may change an 
antecedent in degree, and watch the corresponding 
change in the effect, taking care that no other agent 
influences the effect in the meantime. Often when we 
cannot remove an agent altogether, we may remove it 
in a measurable amount, and observe the result. We 
cannot remove fidction altogether, but the more it is 



Methods of Observation, 331 

diminished, the further will a body travel under the 
impulse of the same force. 

Until a concomitant variation has been fully 
explained, it is merely an empirical law, and any 
inference that it extends at the same rate beyond the 
limits of observation must be made with due caution. 
" Parallel variation," says Professor Bain, ** is some- 
times interrupted by critical points, as in the expansion 
of bodies by heat, which suffers a reverse near the 
point of cooling. Again, the energy of a solution 
does not always follow the strength; very dilute 
solutions occasionally exercise a specific power not 
possessed in any degree by stronger. So, in the 
animal body, food and stimulants operate proportionally 
up to a certain point, at which their further operation 
is checked by the peculiarities in the structure of the 
living organs. . . . We cannot always reason from 
a few steps in a series to the whole series, partly 
because of the occurrence of critical points, and partly 
from the development at the extremes of new and 
unsuspected powers. Sir John Herschel remarks that 
until very recently * the formulae empirically deduced 
for the elasticity of steam, those for the resistance of 
fluids, and on other similar subjects, have almost 
invariably failed to support the theoretical structures 
that have been erected upon them '." * 

II. — Single Residue. 

Subduct from any phenomenon such part as previous induction 
has shown to be the effect of certain antecedents, and the 
residue of the phenomenon is the effect of the remaining 
antecedents. 

" Complicated phenomena, in which several causes 
^ Bain's Logic^ vol. ii. p. 64. 



33* Inductive Logfc^ or the Logw of Science. 

concurring, opposing, or quite independent of each 
other, operate at once, so as to produce a compound 
effect, may be simplified by subducting the effect of all 
the known causes, as well as the nature of the case 
permits, either by deductive reasoning or by appeal to 
experience, and thus leaving as it were a residual 
phenomenon to be explained. It is by this process, in 
fact, that science, in its present advanced state, is 
chiefly promoted. Most of the phenomena which 
nature presents are very complicated ; and when the 
effects of all known causes are estimated with exact- 
ness, and subducted, the residual facts are constantly 
appearing in the form of phenomena altogether new, 
and leading to the most important conclusions." ^ 

It is obvious that this is not a primary method of 
observation, but a method that may be employed with 
great effect to guide observation when a considerable 
advance has been made in accurate knowledge of 
agents and their mode of operation. The greatest 
triumph of the method, the discovery of the planet 
Neptune, was won some years after the above passage 
from Herschel's Discourse was written. Certain per- 
turbations were observed in the movements of the 
planet Uranus : that is to say, its orbit was found not 
to correspond exactly with what it should be when 
calculated according to the known influences of the 
bodies then known to astronomers. These perturba- 
tions were a residual phenomenon. It was supposed 
that they might be due to the action of an unknown 
planet, and two astronomers, Adams and Le Verrier, 
simultaneously calculated the position of a body such 
as would account for the observed deviations. When 

^ Herschers Discourse^ § 158. 



Methods of Observation. 333 

telescopes were directed to the spot thus indicated, the 
planet Neptune waa discovered. This was in Sep- 
tember, 1846 : before its actual discovery, Sir John 
Hersche! exulted in the prospect of it in language that 
strikingly expresses the power of the method. ** We 
see it," he said, "as Columbus saw America from 
the shores of Spain. Its movements have been felt, 
trembling along the far-reaching line of our analysis, 
with a certainty hardly inferior to that of ocular 
demonstration." * 

Many of the new elements in Chemistry have been 
discovered in this way. For example, when distinctive 
spectrums had been observed for all known substances, 
then on the assumption that every substance has a 
distinctive spectrum, the appearance of lines not refer- 
able to any known substance indicated the existence 
of hitherto undiscovered substances and directed search 
for them. Thus Bunsen in i860 discovered two new 
alkaline metals, Caesium and Rubidium. He was 
examining alkalies left from the evaporation of a large 
quantity of mineral water from Durkheim. On apply- 
ing the spectroscope to the flame which this particular 
salt or mixture of salts gave off, he found that some 
bright lines were visible which he had never observed 
before, and which he knew were not produced either 
by potash or soda. He then set to work to analyse 
the mixture, and ultimately succeeded in separating 
two new alkaline substances. When he had succeeded 
in getting them separate, it was of course by the 
Method of Difference that he ascertained them to be 
capable of producing the lines that had excited his 
curiosity. 

1 De Morgan's Budget of Paradox€S^ p. 237, 



Chapter VII, 

THE METHOD OF EXPLANATION. 

Given perplexity as to the cause of any phenomenon, 
what is our natural first step ? We may describe it as 
searching for a clue : we look carefully at the circum- 
stances with a view to finding some means of assimi- 
lating what perplexes us to what is already within our 
knowledge. Our next step is to make a guess, or 
conjecture, or, in scientific language, a hypothesis. 
We exercise our Reason or Nous,^ or Imagination, or 
whatever we choose to call the faculty, and try to 
conceive some cause that strikes us as sufficient to 
account for the phenomenon. If it is not at once 
manifest that this cause has really operated, our third 
step is to consider what appearances ought to present 
themselves if it did operate. We then return to the 
facts in question, and observe whether those appear- 
ances do present themselves. If they do, and if there 
is no other way of accounting for the effect in all its 
circumstances, we conclude that our guess is correct, 
that our hypothesis is proved, that we have reached a 
satisfactory explanation. 

These four steps or stages may be distinguished in 
most protracted inquiries into cause. They correspond 
to the four stages of what Mr. Jevons calls the Induc- 
tive Method par excellence^ Preliminary Observation, 

(334) 



The Method of Explanation. 335 

Hypothesis, Deduction and Verification. Seeing that 
the word Induction is already an overloaded drudge, 
perhaps it would be better to call these four stages the 
Method of Explanation. The word Induction, if we 
keep near its original and most established meaning, 
would apply strictly only to the fourth stage, the 
Verification, the bringing in of the facts to confirm our 
hypothesis. We might call the method the Newtonian 
method, for all four stages are marked in the prolonged 
process by which he made good his theory of Gravitation. 
To give the name of Inductive Method simply to all 
the four stages of an orderly procedure from doubt to a 
sufficient explanation is to encourage a widespread 
misapprehension. There could be no greater error 
than to suppose that only the senses are used in 
scientific investigation. There is no error that men of 
science are so apt to resent in the mouths of the non- 
scientific. Yet they have partly brought it on them- 
selves by their loose use of the word Induction, which 
they follow Bacon in wresting from the traditional 
meaning of Induction, using it to cover both Induction 
or the bringing in of facts — an affair mainly of Obser- 
vation — and Reasoning, the exercise of Nous, the 
process of constructing satisfactory hypotheses. In 
reaction against the popular misconception which 
Bacon encouraged, it is fashionable now to speak of the 
use of Imagination in Science. This is well enough 
polemically. Imagination as commonly understood is 
akin to the constructive faculty in Science, and it is 
legitimate warfare to employ the familiar word of high 
repute to force general recognition of the truth. But 
in common usage Imagination is appropriated to 
creative genius in the Fine Arts, and to speak of 
Imagination in Science is to suggest that Science 



336 Inductive Zogu^ or the Logic of Science, 

deals in fictions, and has discarded Newton's declara- 
tion Hypotheses non Jingo. In a fight for popular 
respect, men of science may be right to claim for 
themselves Imagination ; but in the interests of clear 
understanding, the logician must deplore that they 
should defend themselves from a charge due to their 
abuse of one word by making an equally unwarrantable 
and confusing extension of another. 

Call it what we will, the faculty of likely guessing, 
of making probable hypotheses, of conceiving in all its 
circumstances the past situation or the latent and 
supramicroscopical situation out of which a phenome- 
non has emerged, is one of the most important of the 
scientific man's special gifts. It is by virtue of it that 
the greatest advancements of knowledge have been 
achieved, the cardinal discoveries in Molar and 
Molecular Physics, Biology, Geology, and all depart- 
ments of Science. We must not push the idea ol 
stages in explanatory method too far : the right 
explanation may be reached in a flash. The idea of 
stages is really useful mainly in trying to make clear 
the various difiiculties in investigation, and the fact 
that diff*erent men of genius may show different powers 
in overcoming them. The right hypothesis may occur 
in a moment, as if by simple intuition, but it may be 
tedious to prove, and the gifts that tell in proof, such 
as Newton's immense mathematical power in calculat- 
ing what a hypothesis implies, Darwin's patience in 
verifying, Faraday's ingenuity in devising experiments, 
are all great gifts, and may be serviceable at different 
stages. But without originality and fertility in 
probable hypothesis, nothing can be done. 

The dispute between Mill and Whewell as to the 
place and value of hypotheses in science was in the 



TAe Method of Explanation. 337 

ftiain a dispute about words. Mill did not really 
undervalue hypothesis, and he gave a most luminous 
and accurate account of the conditions of proof. But 
here and there he incautiously spoke of the " hypo- 
thetical method " (by which he meant what we have 
called the method of Explanation) as if it were a 
defective kind of proof, a method resorted to by science 
when the "experimental methods" could not be 
applied. Whether his language fairly bore this con- 
struction is not worth arguing, but this was manifestly 
the construction that Whewell had in his mind when 
he retorted, as if in defence of hypotheses, that " the 
inductive process consists in framing successive 
hypotheses, the comparison of these with the ascer- 
tained facts of nature, and the introduction into them 
of such modifications as the comparison may render 
necessary". This is a very fair description of the 
whole method of explanation. There is nothing really 
inconsistent with it in Mill's account of his " hypo- 
thetical method " ; only he erred himself or was the 
cause of error in others in suggesting, intentionally or 
unintentionally, that the Experimental Methods were 
different methods of proof. The *' hypothetical method," 
as he described it, consisting of Induction, Ratiocina- 
tion, and Verification, really comprehends the principles 
of all modes of observation, whether naturally or arti- 
ficially experimental. We see this at once when we 
ask how the previous knowledge is got in accordance 
with which hypotheses are framed. The answer must 
be, by Observation. However profound the calcula- 
tions, it must be from observed laws, or supposed 
analogues of them, that we start. And it is always by 
Observation that the results of these calculations are 
verified. 



338 Inductive Logic^ or the Logic of Science. 

Both Mill and Whewell, however, confined them« 
selves too exclusively to the great hypotheses of the 
Sciences, such as Gravitation and the Undulatory 
Theory of Light. In the consideration of scientific 
method, it is a mistake to confine our attention to 
these great questions, which from the multitude of 
facts embraced can only be verified by prolonged and 
intricate inquiry. Attempts at the explanation of the 
smallest phenomena proceed on the same plan, and the 
verification of conjectures about them is subject to 
the same conditions, and the methods of investigation 
and the conditions of verification can be studied most 
simply in the smaller cases. Further, I venture to 
think it a mistake to confine ourselves to scientific 
inquiry in the narrow sense, meaning thereby inquiry 
conducted within the pale of the exact sciences. For 
not merely the exact sciences but all men in the 
ordinary affairs of life must follow the same methods 
or at least observe the same principles and conditions, 
in any satisfactory attempt to explain. 

Tares appear among the wheat. Good seed was 
sown : whence, then, come the tares ? " An enemy 
has done this." If an enemy has actually been 
observed sowing the tares, his agency can be proved 
by descriptive testimony. But if he has not been seen 
in the act, we must resort to what is known in Courts 
of Law as circumstantial evidence. This is the 
'* hypothetical method" of science. That the tares 
are the work of an enemy is a hypothesis : we examine 
all the circumstances of the case in order to prove, by 
inference from our knowledge of similar cases, that 
thus, and thus only, can those circumstances be 
accounted tor. Similarly, when a question is raised as 
to the authorship of an anonymous book. We first 



The Mithod of Explanation. 339 

search for a clue by carefully noting the diction, the 
structure of the sentences, the character and sources of 
the illustration, the special tracks of thought. We 
proceed upon the knowledge that every author has 
characteristic turns of phrase and imagery and 
favourite veins of thought, and we look out for such 
internal evidence of authorship in the work before us. 
Special knowledge and acumen may enable us to 
detect the authorship at once from the general resem- 
blance to known work. But if we would have clear 
proof, we must show that the resemblance extends to 
all the details of phrase, structure and imagery: we 
must show that our hypothesis of the authorship of 
XYZ explains all the circumstances. And even this 
is not sufficient, as many erroneous guesses from 
internal evidence may convince us. We must estab- 
lish further that there is no other reasonable way of 
accounting for the matter and manner of the book ; for 
example, that it is not the work of an imitator. An 
imitator may reproduce all the superficial peculiarities 
of an author with such fidelity that the imitation can 
hardly be distinguished from the original: thus few 
can distinguish between Fenton's work and Pope's in 
the translation of the Odyssey. We must take such 
known facts into account in deciding a hypothesis of 
authorship. Such hypotheses can seldom be decided 
on internal evidence alone: other circumstantial evi- 
dence — other circumstances that ought to be discover- 
able if the hypothesis is correct — must be searched for. 
The operation of causes that are manifest only in 
their effects must be proved by the same method as the 
operation of past causes that have left only their effects 
behind them. Whether light is caused by a projection 
^ p&rticlss from a luminous body or by an agitation 



340 Inductive Logic, or the Logic of Science. 

communicated through an intervening medium cannot 
be directly observed. The only proof open is to 
calculate what should occur on either hypothesis, and 
observe whether this does occur. In such a case there 
is room for the utmost calculating power and experi- 
mental ingenuity. The mere making of the general 
hypothesis or guess is simple enough, both modes of 
transmitting influence, the projection of moving matter 
and the travelling of an undulation or wave movement, 
being familiar facts. But it is not so easy to calculate 
exactly how a given impulse would travel, and 
what phenomena of ray and shadow, of reflection, 
refraction and diffraction ought to be visible in its 
progress. Still, no matter how intricate the calcula- 
tion, its correspondence with what can be observed is 
the only legitimate proof of the hypothesis. 



IL — Obstacles to Explanation. — Plurality of 
Causes and Intermixture of Effects. 

There are two main ways in which explanation may 
be baffled. There may exist more than one cause 
singly capable of producing the effect in question, and 
we may have no means of determining which of the 
equally sufficient causes has actually been at work. 
For all that appears the tares in our wheat may be 
the effect of accident or of malicious design : an 
anonymous book may be the work of an original author 
or of an imitator. Again, an effect may be the joint 
result of several co-operating causes, and it may be 
impossible to determine their several potencies. The 
bitter article in the Quarterly may have helped to kill 
John Keats, but it co-operated with an enfeebled 



The Method of Explanation, 341 

constitution and a naturally over- sensitive temperament, 
and we cannot assign its exact weight to each of these 
coefficients. Death may be the result of a combina- 
tion of causes ; organic disease co-operating with 
exposure, over-fatigue co-operating with the enfeeble- 
ment of the system by disease. 

The technical names for these difficulties, Plurality 
of Causes and Intermixture of Effects, are apt to con- 
fuse without some clearing up. In both kinds of 
difficulty more causes than one are involved : but in 
the one kind of case there is a plurality of possible or 
equally probable causes, and we are at a loss to decide 
which : in the other kind of case there is a plurality of 
co-operating causes ; the effect is the result or product 
of several causes working conjointly, and we are unable 
to assign to each its due share. 

It is with a view to overcoming these difficulties 
that Science endeavours to isolate agencies and ascer- 
tain what each is capable of singly. Mill and Bain 
treat Plurality of Causes and Intermixture of Effects 
in connexion with the Experimental Methods. It is 
better, perhaps, to regard them simply as obstacles to 
explanation, and the Experimental Methods as methods 
of overcoming those obstacles. The whole purpose of 
the Experimental Methods is to isolate agencies and 
effects : unless they can be isolated, the Methods are 
inapplicable. In situations where the effects observable 
may be referred with equal probability to more than 
one cause, you cannot eliminate so as to obtain a 
single agreement. The Method of Agreement is 
frustrated. And an investigator can get no light from 
mixed effects, unless he knows enough of the causes at 
work to be able to apply the Method of Residues. If 
he does not, he must simply look out for or devise 



343 Inductive Logiq or the Lagk of Sdena, 

instances where the agencies are at work separately, 
and apply the principle of Single Difference. 

Great, however, as the difficulties are, the theory of 
Plurality and Intermixture baldly stated makes them 
appear greater than they are in practice. There is a 
consideration that mitigates the complication, and 
renders the task of unravelling it not altogether 
hopeless. This is that different causes have distinctive 
ways of operating, and leave behind them marks of 
their presence by which their agency in a given case 
may be recognised. 

An explosion, for example, occurs. There are 
several explosive agenciesj capable of causing as much 
destruction as meets the eye at the first glance. The 
agent in the case before us may be gunpowder or it 
may be dynamite. But the two agents are not so 
alike in their mode of operation as to produce results 
identical in every circumstance. The expert inquirer 
knows by previous observation that when gunpowder 
acts the objects in the neighbourhood are blackened ; 
and that an explosion of dynamite tears and shatters in 
a way peculiar to itself. He is thus able to interpret 
the traces, to make and prove a hypothesis. 

A man's body is found dead in water. It may be 
a question whether death came by drowning or by 
previous violence. He may have been suffocated and 
afterwards thrown into the water. But the circum- 
stances will tell the true story. Death by drowning 
has distinctive symptoms. If drowning was the cause, 
water will be found in the stomach and froth in the 
trachea. 

Thus, though there may be a plurality of possible 
causes, the causation in the given case may be brought 
home to one by distinctive accompaniments, and it is 



The Metkod of Explanation. 343 

the business of the scientific inquirer to study these. 
What is known as the ** ripple-mark '* in sandstone 
surfaces may be produced in various ways. The most 
familiar way is by the action of the tides on the sand 
of the sea-shore, and the interpreter who knows this 
way only would ascribe the marks at once to this 
agency. But ripple-marks are produced also by the 
winds on drifting sands, by currents of water where no 
tidal influence is felt, and in fact by any body of watei 
in a state of oscillation. Is it, then, impossible to 
decide between these alternative possibilities of 
causation ? No : wind-ripples and current-ripples and 
tidal-ripples have each their own special character and 
accompanying conditions, and the hypothesis of one 
rather than another may be made good by means of 
these. *' In rock-formations," Mr. Page says,^ ** there 
are many things which at first sight seem similar, 
and yet on more minute examination, differences are 
detected and conditions discovered which render it 
impossible that these appearances can have arisen 
from the same causation." 

The truth is that generally when we speak of 
plurality of causes, of alternative possibilities of causa* 
tion, we are not thinking of the effect in its individual 
entirety, but only of some general or abstract aspect 
of it When we say, e,g,y that death may be produced 
by a great many different causes, poison, gunshot 
wounds, disease of this or that organ, we are thinking 
of death in the abstract, not of the particular case 
under consideration, which as an individual case, has 
characters so distinctive that only one combination of 
causes is possible. 

^ Page's Philosophy of Geology^ p. 38, 



344 Indi4ctive Logic^ or the Logic of Science. 

The effort of science is to become less and less 
abstract in this sense, by observing agencies or com- 
binations of agencies apart and studying the special 
characters of their effects. That knowledge is then 
applied, on the assumption that where those characters 
are present, the agent or combination of agencies has 
been at work. Given an effect to be explained, it is 
brought home to one out of several possible alternatives 
by circumstantial evidence. 

Bacon's phrase, Instantia Crucis^ or Finger-post 
Instance, might be conveniently appropriated as a 
technical name for a circumstance that is decisive 
between rival hypotheses. This was, in effect, pro- 
posed by Sir John Herschel,' who drew attention to 
the importance of these crucial instances, and gave the 
following example: "A curious example is given by 
M. Fresnel, as decisive, in his mind, of the question 
between the two great opinions on the nature of light, 
which, since the time of Newton and Huyghens, have 
divided philosophers. When two very clean glasses 
are laid one on the other, if they be not perfectly flat, 
but one or both in an almost imperceptible degree 
convex or prominent, beautiful and vivid colours will 
be seen between them ; and if these be viewed through 
a red glass, their appearance will be that of alternate 
dark and bright stripes. . . . Now, the coloured stripes 
thus produced are explicable on both theories, and are 
appealed to by both as strong confirmatory facts ; but 
there is a difference in one circumstance according as 
one or the other theory is employed to explain them. 
In the case of the Huyghenian doctrine, the intervals 

1 Crux in this phrase means a cross erected at the parting of 
ways, with arms to tell whither each way leads. 
a Discourse^ § 2i8» 



The Method of Explanation, 345 

between the bright stripes ought to appear absolutely 
black; in the other, half bright^ when viewed [in a 
particular manner] through a prism. This curious 
case of difference was tried as soon as the opposing 
consequences of the two theories were noted by M. 
Fresnel, and the result is stated by him to be decisive 
in favour of that theory which makes light to consist 
in the vibrations of an elastic medium.** 



III. — The Proof op a Hypothesis. 

The completest proof of a hypothesis is when that 
which has been hypothetically assumed to exist as a 
means of accounting for certain phenomena is after- 
wards actually observed to exist or is proved by 
descriptive testimony to have existed. Our argument, 
for example, from internal evidence that Mill in writing 
his Logic aimed at furnishing a method for social 
investigations is confirmed by a letter to Miss Caroline 
Fox, in which he distinctly avowed that object. 

The most striking example of this crowning verifi- 
cation in Science is the discovery of the planet 
Neptune, in which case an agent hypothetically 
assumed was actually brought under the telescope as 
calculated. Examples almost equally striking have 
occurred in the history of the Evolution doctrine. 
Hypothetical ancestors with certain peculiarities of 
structure have been assumed as links between living 
species, and in some cases their fossils have actually 
been found in the geological register. 

Such triumphs of verification are necessarily rare. 
For the most part the hypothetical method is applied 
to cases where proof by actual observation is impossible, 
^uqh as prehistoric conditions of the earth or of life 



34^ Inductive LogiCy or the Logic of Science. 

upon the earth, or conditions in the ultimate constitu^ 
tion of matter that are beyond the reach of the strongest 
microscope. Indeed, some would confine the word 
hypothesis to cases of this kind. This, in fact, was 
done by Mill : hypothesis, as he defined it, was a con- 
jecture not completely proved, but with a large amount 
of evidence in its favour. But seeing that the proce- 
dure of investigation is the same, namely, conjecture, 
calculation and comparison of facts with the calculated 
results, whether the agency assumed can be brought 
to the test of direct observation or not, it seems better 
not to restrict the word hypothesis to incompletely 
proved conjectures, but to apply it simply to a conjec- 
ture made at a certain stage in whatever way it may 
afterwards be verified. 

In the absence of direct verification, the proof of 
a hypothesis is exclusive sufficiency to explain the 
circumstances. The hypothesis must account for all 
the circumstances, and there must be no other way of 
accounting for them. Another requirement was men- 
tioned by Newton in a phrase about the exact meaning 
of which there has been some contention. The first 
of his Regulae Philosophandi laid down that the cause 
assumed must be a vera causa. " We are not," the 
Rule runs, ^' to admit other causes of natural things 
than such as both are true, and suffice for explaining 
their phenomena." ^ 

It has been argued that the requirement of ** verity " 
is superfluous ; that it is really included in the require- 
ment of sufficiency; that if a cause is sufficient to 
explain the phenomena it must ipso facto be the true 



^Causae rerum naturalium non plures admitti debere quam 
quse et verae sint et earum phenomenis expHcandis sufficiant. 



The Method of Explanation, 347 

cause. This may be technically arguable, given a 
sufficient latitude to the word sufficiency : nevertheless, 
it is convenient to distinguish between mere sufficiency 
to explain the phenomena in question, and the proof 
otherwise that the cause assigned really exists in rerum 
natura, or that it operated in the given case. The 
frequency with which the expression vera causa has 
been used since Newton's time shows that a need is 
felt for it, though it»may be hard to define " verity " 
precisely as something apart from " sufficiency ". If we 
examine the common usage of the expression we shall 
probably find that what is meant by insisting on a vera 
causa is that we must have some evidence for the cause 
assigned outside the phenomena in question. In 
seeking for verification of a hypothesis we must extend 
our range beyond the limited facts that have engaged 
our curiosity and that demand explanation. 

There can be little doubt that Newton himself aimed 
his rule at the Cartesian hypothesis of Vortices. This 
was an attempt to explain the solar system on the 
hypothesis that cosmic space is filled with a fluid in 
which the planets are carried round as chips of wood 
in a whirlpool, or leaves or dust in a whirlwind. Now 
this is so far a vera causa that the action of fluid 
vortices is a familiar one : we have only to stir a cup 
of tea with a bit of stalk in it to get an instance. The 
agency supposed is sufficient also to account for the 
revolution of a planet round the sun, given sufficient 
strength in the fluid to buoy up the planet. But if 
there were such a fluid in space there would be other 
phenomena : and in the absence of these other 
phenomena the hypothesis must be dismissed as 
imaginary. The fact that comets pass into and out 
of spaces where the vortices must be assumed to be 



348 Inductive Logic^ or the Logic of Scieme. 

in action without exhibiting any perturbation is an 
instaniia crucis against the hypothesis. 

If by the requirement of a vera causa were meant 
that the cause assigned must be one directly open to 
observation, this would undoubtedly be too narrow a 
limit. It would exclude such causes as the ether which 
is assumed to fill interstellar space as a medium 
for the propagation of light. The only evidence for 
such a medium and its various properties is sufficiency 
to explain the phenomena. Like suppositions as to 
the ultimate constitution of bodies, it is of the nature 
of what Professor Bain calls a " Representative 
Fiction '' : the only condition is that it must explain all 
the phenomena, and that there must be no other way of 
explaining all. When it is proved that light travels 
with a finite velocity, we are confined to two alternative 
ways of conceiving its transmission, a projection ol 
matter from the luminous body and the transference of 
vibrations through an intervening medium. Either 
hypothesis would explain many of the facts : our 
choice must rest with that which best explains all. 
But supposing that all the phenomena of light were 
explained by attributing certain properties to this 
intervening medium, it would probably be held that 
the hypothesis of an ether had not been fully verified 
till other phenomena than those of light had been 
shown to be incapable of explanation on any other 
hypothesis. If the properties ascribed to it to explain 
the phenom.ena of light sufficed at the same time to 
explain otherwise inexplicable phenomena connected 
with Heat, Electricity, or Gravity, the evidence of its 
reality would be greatly strengthened. 

Not only must the circumstances in hand be 
explained, but other circumstances must be found to 



Trhe Method of Explanation, 349 

be such as we should expect if the cause assigned 
really operated. Take, for example, the case of 
Erratic blocks or boulders, huge fragments of rock 
found at a distance from their parent strata. The 
lowlands of England, Scotland, and Ireland, and the 
great central plain of Northern Europe contain many 
such fragments. Their composition shows indubitably 
that they once formed part of hills to the northward of 
their present site. They must somehow have been 
detached and transported to where we now find them. 
How ? One old explanation is that they were carried 
by witches, or that they were themselves witches acci- 
dentally dropped and turned into stone. Any such 
explanation by supernatural means can neither be 
proved nor disproved. Some logicians would exclude 
such hypotheses altogether on the ground that they 
cannot be rendered either more or less probable by subse- 
quent examination.^ The proper scientific limit, how- 
ever, is not to the making of hypotheses, but to the 
proof of them. The more hypotheses the merrier : 
only if such an agency as witchcraft is suggested, we 
should expect to find other evidence of its existence in 
other phenomena that could not otherwise be explained 
Again, it has been suggested that the erratic boulders 
may have been transported by water. Water is so far 
a vera causa that currents are known to be capable of 
washing huge blocks to a great distance. But blocks 
transported in this way have the edges worn off by the 
friction of their passage : and, besides, currents strong 
enough to dislodge and force along for miles blocks 
as big as cottages must have left other marks of their 



^ See Prof. Fowler on the Conditions of Hypotheses, Inductive 
Logic^ pp. X0O-ZI5. 



35© Inductive Logic^ or the Logic of Science. 

presence. The explanation now received is that 
glaciers and icebergs were the means of transport 
But this explanation was not accepted till multitudes 
of circumstances were examined all tending to show 
that glaciers had once been present in the regions 
where the erratic blocks are found. The minute habits 
of glaciers have been studied where they still exist : 
how they slowly move down carrying fragments of 
rock ; how icebergs break off when they reach water, 
float off with their load, and drop it when they melt; 
how they grind and smooth the surfaces of rocks over 
which they pass or that are frozen into them : how 
they undercut and mark the faces of precipices past 
which they move ; how moraines are formed at the 
melting ends of them, and so forth. When a district 
exhibits all the circumstances that are now observed 
to attend the action of glaciers the proof of the 
hypothesis that glaciers were once there is complete. 



Chapter VIIL 

SUPPLEMENTARY METHODS OF INVESTIGATION. 

I. — The Maintenance of Averages. — Supplement 
TO THE Method of Difference. 

A CERTAIN amount of law obtains among events that 
are usually spoken of as matters of chance or accident 
in the individual case. Every kind of accident recurs 
with a certain uniformity. If we take a succession of 
periods, and divide the total number of any kind of 
event by the number of periods, we get what is called 
the average for that period : and it is observed that 
such averages are maintained from period to period. 
Over a series of years there is a fixed proportion 
between good harvests and bad, between wet days and 
dry : every year nearly the same number of suicides 
takes place, the same number of crimes, of accidents 
to life and limb, even of suicides, crimes, or injuries by 
particular means : every year in a town nearly the 
same number of children stray from their parents and 
are restored by the police : every year nearly the same 
number of persons post letters without putting an 
address on them. 

This maintenance of averages is simple matter of 
observation, a datum of experience, an empirical law. 
Once an average for any kind of event has been 
noted, we may count upon its continuance as we count 
upon the continuance of any other kind of observed 

(351) 



35^ Inductive Logic^ or the Logic of Science. 

uniformity. Insurance companies proceed upon such 
empirical laws of average in length of life and 
immunity from injurious accidents by sea or land : 
their prosperity is a practical proof of the correctness 
and completeness of the observed facts and the sound- 
ness of their inference to the continuance of the average. 

The constancy of averages is thus a guide in prac- 
tice. But in reasoning upon them in investigations of 
cause, we make a further assumption than continued 
uniformity. We assume that the maintenance of the 
average is due to the permanence of the producing 
causes. We regard the average as the result of the 
operation of a limited sum of forces and conditions, 
incalculable as regards their particular incidence, but 
always pressing into action, and thus likely to operate 
a certain number of times within a limited period. 

Assuming the correctness of this explanation, it 
would follow that any change in the average is due to 
some change in the producing conditions ; and this deriva- 
tive law is applied as a help in the observation and | 
explanation of social facts. Statistics are collected 
and classified : averages are struck : and changes in 
the average are referred to changes in the concomitant 
conditions. ! 

With the help of this law, we may make a near 
approach to the precision of the Method of Difference. 
A multitude of unknown or unmeasured agents may ' 
be at work on a situation, but we may accept the i 
average as the result of their joint operation. If then i 
a new agency is introduced or one of the known agents ^ 
is changed in degree, and this is at once followed by a i 
change in the average, we may with fair probability 
refer the change in the result to the change in the 
antecedents. 



Supplementary Methods of TtVDesttgatton, 353 

The difficulty is to find a situation where only one 
antecedent has been changed before the appearance 
of the effect. This difficulty may be diminished in 
practice by eliminating changes that we have reason 
to know could not have affected the circumstances in 
question. Suppose, for example, our question is 
whether the Education Act of 1872 had an influence 
in the decrease of juvenile crime. Such a decrease 
took place post hoc; was it propter hoc? We may at 
once eliminate or put out of account the abolition of 
Purchase in the Army or the extension of the Franchise 
as not having possibly exercised any influence on 
juvenile crime. But with all such eliminations, there 
may still remain other possible influences, such as an 
improvement in the organisation of the Police, or an 
expansion or contraction of employment. " Can you 
tell me in the face of chronology," a leading statesman 
once asked, ** that the Crimes Act of 1887 did not 
diminish disorder in Ireland ? " But chronological 
sequence alone is not a proof of causation as long as 
there are other contemporaneous changes of condition 
that may also have been influential. 

The great source of fallacy is our proneness to 
eliminate or isolate in accordance with our prejudices. 
This has led to the gibe that anything can be proved 
by statistics. Undoubtedly statistics may be made to 
prove anything if you have a sufficiently low standard 
of proof and ignore the facts that make against your 
conclusion. But averages and variations in them are 
instructive enough if handled with due caution. The 
remedy for rash conclusions from statistics is not no 
statistics, but more of them and a sound knowledge of 
the conditions of reasonable proot 



23 



354 Inductive Logic^ or the Logic of Sciena, 

IL-— The Presumption from Extra-Casual 
Coincidence. 

We have seen that repeated coincidence raises a 
presumption of causal connexion between the coincid- 
ing events. If we find two events going repeatedly 
together, either abreast or in sequence, we infer that 
the two are somehow connected in the way of causa- 
tion, that there is a reason for the coincidence in the 
manner of their production. It may not be that the 
one produces the other, or even that their causes are 
in any way connected : but at least, if they are inde- 
pendent one of the other, both are tied down to happen 
at the same place and time, — the coincidence of both 
with time and place is somehow fixed. 

But though this is true in the main, it is not true 
without qualification. We expect a certain amount of 
repeated coincidence without supposing causal con- 
nexion. If certain events are repeated very often 
within our experience, if they have great positive 
frequency, we may observe them happening together 
more than once without concluding that the coincidence 
is more than fortuitous. 

For example, if we live in a neighbourhood possessed 
of many black cats, and sally forth to our daily business 
in the morning, a misfortune in the course of the day 
might more than once follow upon our meeting a 
black cat as we went out without raising in our minds 
any presumption that the one event was the result of 
the other. 

Certain planets are above the horizon at certain 
periods of the year and below the horizon at certain 
other periods. All through the year men and women 
are born who afterwards achieve distinction in various 



Supplementary Methods of Investigation. 355 

walks of life, in love, in war, in business, at the bar, 
in the pulpit. We perceive a certain number of 
coincidences between the ascendancy of certain planets 
and the birth of distinguished individuals without 
suspecting that planetary influence was concerned in 
their superiority. 

Marriages take place on all days of the year: the 
sun shines on a good many days at the ordinary time 
for such ceremonies ; some marriages are happy, some 
unhappy; but though in the case of many happy 
marriages the sun has shone upon the bride, we regard 
the coincidence as merely accidental. 

Men often dream of calamities and often suffer 
calamities in real life : we should expect the coinci- 
dence of a dream of calamity followed by a reality to 
occur more than once as a result of chance. There 
are thousands of men of different nationalities in 
business in London, and many fortunes are made : we 
should expect more than one man of any nationality 
represented there to make a fortune without arguing 
any connexion between his nationality and his success. 

We allow, then, for a certain amount of repeated 
coincidence without presuming causal connexion : can 
any rule be laid down for determining the exact 
amount ? 

Prof. Bain has formulated the following rule : 
" Consider the positive frequency of the phenomena 
themselves, and how great frequency of coincidence 
must follow from that, supposing there is neither con- 
nexion nor repugnance. If there be greater frequency, 
there is connexion; if less, repugnance." 

I do not know that we can go further definite in 
precept. The number of casual coincidences bears a 
certain proportion to the positive frequency of the 



35^ Inductive Logic^ or t/u Logic of Sciena. 

coinciding phenomena : that proportion is to be deter- 
mined by common-sense in each case. It may be 
possible, however, to bring out more clearly the prin- 
ciple on which common-sense proceeds in deciding 
what chance will and will not account for, although 
our exposition amounts only to making more clear 
what it is that we mean by chance as distinguished 
from assignable reason. I would suggest that in 
deciding what chance will not account for, we make 
regressive application of a principle which may be 
called the principle of Equal and Unequal Alternatives, 
and which may be worded as follows : — 

Of a given number of possible alternatives, all equally 
possible, one of which is bound to occur at a given 
time, we expect each to have its turn an equal 
number of times in the long run. If several of the 
alternatives are of the same kind, we expect an 
alternative of that kind to recur with a frequencj 
proportioned to their greater number. If any ol 
the alternatives has an advantage, it will recur with 
a frequency proportioned to the strength of that 
advantage. 

Situations in which alternatives are absolutely equal 
are rare in nature, but they are artificially created for 
games " of chance," as in tossing a coin, throwing 
dice, drawing lots, shuffling and dealing a pack of 
cards. The essence of all games of chance is to con- 
struct a number of equal alternatives, making them as 
nearly equal as possible, and to make no prearrange- 
ment which of the number shall come off. We then 
say that this is determined by chance. If we ask why 
we believe that when we go on bringing off one alter- 
native at a time, each will have its turn, part of 



Supplementary Methods of Investigation, 357 

the answer undoubtedly is that given by De Morgan, 
namely, that we know no reason why one should be 
chosen rather than another. This, however, is probably 
not the whole reason for our belief. The rational 
belief in the matter is that it is only in the long run 
or on the average that each of the equal alternatives 
will have its turn, and this is probably founded on the 
experience of actual trial. The mere equality of the 
alternatives, supposing them to be perfectly equal, 
would justify us as much in expecting that each would 
have its turn in a single revolution of the series, in one 
complete cycle of the alternatives. This, indeed, may 
be described as the natural and primitive expectation 
which is corrected by experience. Put six balls in a 
wicker bottle, shake them up, and roll one out : return 
this one^ and repeat the operation : at the end of six 
draws we might expect each ball to have had its turn of 
being drawn if we went merely on the abstract equality 
of the alternatives. But experience shows us that in 
six successive draws the same ball may come out 
twice or even three or four times, although when 
thousands of drawings are made each comes out nearly 
an equal number of times. So in tossing a coin, 
heads may turn up ten or twelve times in succession, 
though in thousands of tosses heads and tails are 
nearly equal. Runs of luck are thus within the 
rational doctrine of chances : it is only in the long run 
that luck is equalised supposing that the events are 
pure matter of chance, that is, supposing the funda- 
mental alternatives to be equal. 

If three out of six balls are of the same colour, we 
expect a ball of that colour to come out three times as 
often as any other colour on the average of a long 
succession of tries. This illustrates the second clause 



35 S InSmtive Logic, or the Logic of Science. 

of our principle. The third is illustrated by a loaded 
coin or die. 

By making regressive application of the principle 
thus ascertained by experience, we often obtain a clue 
to special causal connexion. We are at least enabled 
t© isolate a problem for investigation. If we find one 
of a number of alternatives recurring more frequently 
than the others, we are entitled to presume that they 
are not equally possible, that there is some inequality 
in their conditions. 

The inequality may simply lie in the greater possible 
frequency of one of the coinciding events, as when 
there are three black balls in a bottle of six. We 
must therefore discount the positive frequency before 
looking for any other cause. Suppose, for example, 
we find that the ascendancy of Jupiter coincides mora 
frequently with the birth of men afterwards dis- 
tinguished in business than with the birth of men 
otherwise distinguished, say in war, or at the bar, or 
in scholarship. We are not at liberty to conclude 
planetary influence till we have compared the positive 
frequency of the different modes of distinction. 
The explanation of the more frequently repeated 
coincidence may simply be that more men altogether 
are successful in business than in war or law or 
scholarship. If so, we say that chance accounts for 
the coincidence, that is to say, that the coincidence 
casual as far as planetary influence is concerned. 

So in epidemics of fever, if we find on taking a long 
average that more cases occur in some streets of a 
town than in others, we are not warranted in conclud- 
ing that the cause lies in the sanitary conditions of 
those streets or in any special liability to infection 
without first taking into account the number of families 



Supplementary Methods of Investigation. 359 

in the different streets. If one street showed on the 
average ten times as many cases as another, the 
coincidence might still be judged casual if there were 
ten times as many families in it. 

Apart from the fallacy of overlooking the positive 
frequency, certain other fallacies or liabilities to error 
in applying this doctrine of chances may be specified. 

1. We are apt, under the influence of prepossession 
or prejudice, to remember certain coincidences better 
than others, and so to imagine extra-casual coincidence 
where none exists. This bias works in confirming all 
kinds of established beliefs, superstitious and other, 
beliefs in dreams, omens, retributions, telepathic com- 
munications, and so forth. Many people believe that 
nobody who thwarts them ever comes to good, and can 
produce numerous instances from experience in sup- 
port of this belief. 

2. We are apt, after proving that there is a residuum 
beyond what chance will account for on due allowance 
made for positive frequency, to take for granted that we 
have proved some particular cause for this residuum. 
Now we have not really explained the residuum by the 
application of the principle of chances : we have only 
isolated a problem for explanation. There may be 
more than chance will account im : yet the cause may 
not be the cause that we assign off-hand. Take, for 
example, the coincidence that has been remarked 
between race and different forms of Christianity in 
Europe. If the distribution of religious systems were 
entirely independent of race, it might be said that you 
would expect one system to coincide equally often with 
different races in proportion to the positive number 
of their communities. But the Greek system is found 
almost solely among Slavonic peoples, the Roman 



360 Inductive Logic, or the Logic of Science, 

among Celtic, and the Protestant among Teutonic. 
The coincidence is greater than chance will account 
for. Is the explanation then to be found in some 
special adaptability of the religious system to the 
character of the people? This may be the right 
explanation, but we have not proved it by merely dis- 
counting chance. To prove this we must show that 
there was no other cause at work, that character was 
the only operative condition in the choice of system, 
that political combinations, for example, had nothing 
to do with it. The presumption from extra-casual 
coincidence is only that there is a special cause : in 
determining what that is we must conform to the 
ordinary conditions of explanation. 

So coincidence between membership of the Govern- 
ment and a classical education may be greater than 
chance would account for, and yet the circumstance of 
having been taught Latin and Greek at school may 
have had no special influence in qualifying the members 
for their duties. The proportion of classically educated 
in the Government may be greater than the proportion 
of them in the House of Commons, and yet their 
eminence may be in no way due to their education. 
Men of a certain social position have an advantage 
in the competition for office, and all those men have 
been taught Latin and Greek as a matter of course. 
Technically speaking, the coinciding phenomena may 
be independent effects of the same cause. 

3. Where the alternative possibilities are very 
numerous, we are apt not to make due allowance for 
the number, sometimes overrating it, sometimes under- 
rating it. 

The fallacy of underrating the number is often seen 
in games of chance, where the object is to create a vast 



Supplementary Methods of Investigation. 361 

number of alternatives, all equally possible, equally 
open to the player, without his being able to affect 
the advent of one more than another. In whist, for 
example, there are some six billions of possible hands. 
Yet it is a common impression that, one night with 
another, in the course of a year, a player will have 
dealt to him about an equal number of good and bad 
hands. This is a fallacy. A very much longer time 
is required to exhaust the possible combinations. 
Suppose a player to have 2000 hands in the course of 
a year: this is only one '* set," one combination, out 
of thousands of millions of such sets possible. Among 
those millions of sets, if there is nothing but chance 
in the matter, there ought to be all proportions of good 
and bad, some sets all good, some all bad, as well as 
some equally divided between good and bad.* 

Sometimes, however, the number of possible alter- 
natives is overrated. Thus, visitors to London often 
remark that they never go there without meeting some- 
body from their own locality, and they are surprised 
at this as if they had the same chance of meeting their 
fellow-visitors and any other of the four millions of 
the metropolis. But really the possible alternatives 
of rencounter are far less numerous. The places 
frequented by visitors to London are filled by much 
more limited numbers : the possible rencounters are 
to be counted by thousands rather than by millions. 

^ See De Morgan's Es^say on Probabilities^ o* vi., ** On Common 
Notions of Probability ". 



Chapter IX 

PROBABLE INFERENCE TO PARTICULARS —THE 
MEASUREMENT OF PROBABILITY. 

Undoubtedly there are degrees of probability. Not 
only do we expect some events with more confidence 
than others : we may do so, and our confidence may 
be misplaced : but we have reason to expect some 
with more confidence than others. There are different 
degrees of rational expectation. Can those degrees be 
measured numerically? 

The question has come into Logic from the mathe- 
maticians. The calculation of Probabilities is a 
branch of Mathematics. We have seen how it may 
be applied to guide investigation by eliminating what 
is due to chance, and it has been vaguely conceived by 
logicians that what is called the calculus of proba- 
bilities might be found useful also in determining by 
exact numerical measurement the probability of single 
events. Dr. Venn, who has written a separate treatise 
on the Logic of Chance, mentions " accurate quanti- 
tative apportionment of our belief" as one of the goals 
which Logic should strive to attain. The following 
passage will show his drift.* 

A man in good health would doubtless like to know 
whether he will be alive this time next year. The fact 

^Empirical Logic, p. 556. 
(36a) 



Probable Inference to Particulars. 363 

will be settled one way or the other in due time, if he can 
afford to wait, but if he wants a present decision, Statistics 
and the Theory of Probability can alone give him any 
information. He learns that the odds are, say five to 
one that he will survive, and this is an answer to his 
question as far as any answer can be given. Statisticians 
are gradually accumulating a vast mass of data of this 
general character. What they may be said to aim at is to 
place us in the position of being able to say, in any given 
time or place, what are the odds for or against any at 
present indeterminable fact which belongs to a class 
admitting of statistical treatment. 

Again, outside the regions of statistics proper — which 
deal, broadly speaking, with events which can be numbered 
or measured, and which occur with some frequency — there 
is still a large field as to which some better approach 
to a reasoned intensity of belief can be acquired. What 
will be the issue of a coming war ? Which party will win 
in the next election? Will a patient in the crisis of a 
given disease recover or not ? That statistics are lying 
here in the background, and are thus indirectly efficient 
in producing and graduating our belief, I fully hold; but 
there is such a large intermediate process of estimating, 
and such scope for the exercise of a practised judgment, 
that no direct appeal to statistics in the common sense 
can directly help us. In sketching out therefore the 
claims of an Ideal condition of knowledge, we ought 
clearly to include a due apportionment of belief to every 
event of such a class as this. It is an obvious defect that 
one man should regard as almost certain what another 
man regards as almost impossible. Short, therefore, of 
certain prevision of the future, we want complete agree- 
ment as to the degree of probability of every future event: 
and for that matter of every past event as well. 

Technically speaking, if we extend the name 
Modality (see p. 78) to any qualification of the cer- 
tainty of a statement of belief, what Dr. Venn here 



364 Inductive Logic^ or the Logic of Science. 

desiderates, as he has himself suggested, is a more 
exact measurement of the Modality of propositions. 
We speak of things as being certain, possible, impos- 
sible, probable, extremely probable, faintly probable, 
and so forth : taking certainty as the highest degree of 
probability* shading gradually down to the zero of the 
impossible, can we obtain an exact numerical measure 
for the gradations of assurance ? 

To examine the principles of all the cases in which 
chances for and against an occurrence have been cal- 
culated from real or hypothetical data, would be to 
trespass into the province of Mathematics, but a few 
simple cases will serve to show what it is that the 
calculus attempts to measure, and what is the practical 
value of the measurement as applied to the probability 
of a single event. 

Suppose there are 100 balls in a box, 30 white and 
70 black, all being alike except in respect of colour, we 
say that the chances of drawing a black ball as against 
a white are as 7 to 3, and the probability of drawing 
black is measured by the fraction ^^. In believing 
this we proceed on the principle already explained 
(p. 356) of Proportional Chances. We do not know 
for certain whether black or white will emerge, but 
knowing the antecedent situation we expect black 



^ Mr. Jevons held that all infer&nce is merely probable and that 
no inference is certain. But this is a purposeless repudiation of 
common meaning, which he cannot himself consistently adhere 
to. We find him saying that if a penny is tossed into the air it 
will certainly come down on one side or the other, on which 
side being a matter of probability. In common speech probability 
is applied to a degree of belief short of certainty, but to say that 
certainty is the highest degree of probability does no violence to 
the common meaning. 



Probable Inference to Particulars. 365 

rather than white with a degree of assurance corres- 
ponding to the proportions of the two in the box. It 
is our degree of rational assurance that we measure by 
this fraction, and the rationality of it depends on the 
objective condition of the facts, and is the same for all 
men, however much their actual degree of confidence 
may vary with individual temperament. That black 
will be drawn seven times out of every ten on an 
average if we go on drawing to infinity, is as certain 
as any empirical law : it is the probability of a single 
draw that we measure by the fraction ^. 

When we build expectations of single events on 
statistics of observed proportions of events of that 
kind, it is ultimately on the same principle that 
rational expectation rests. That the proportion will 
obtain on the average we regard as certain : the ratio 
of favourable cases to the whole number of possible 
alternatives is the measure of rational expectation 
or probability in regard to a particular occurrence. 
If every year five per cent, of the children of a town 
stray from their guardians, the probability of this or 
that child's going astray is ^. The ratio is a correct 
measure only on the assumption that the average is 
maintained from year to year. 

Without going into the combination of probabilities, 
we are now in a position to see the practical value of 
such a calculus as applied to particular cases. There 
has been some misunderstanding among logicians on 
the point. Mr. Jevons rebuked Mill for speaking dis- 
respectfully of the calculus, eulogised it as one of the 
noblest creations of the human intellect, and quoted 
Butler's saying that "Probability is the guide of life ". 
But when Butler uttered this famous saying he was 
probably not thinking of the mathematical calculus of 



366 Inductive Logic^ or the Logic of Science. 

probabilities as applied to particular cases, and it was 
this special application to which Mill attached com- 
paratively little value. 

The truth is that we seldom calculate or have any 
occasion to calculate individual chances except as a 
matter of curiosity. It is true that insurance offices 
calculate probabilities, but it is not the probability of 
this or that man dying at a particular age. The 
precise shade of probability for the individual, in so 
far as this depends on vital statistics, is a matter of 
indifference to the company as long as the average is 
maintained. Our expectations about any individual 
life cannot be measured by a calculation of the chances 
because a variety of other elements affect those expec- 
tations. We form beliefs about individual cases, but 
we try to get surer grounds for them than the chances 
as calculable from statistical data. Suppose a person 
were to institute a home for lost dogs, he would doubt- 
less try to ascertain how many dogs were likely to go 
astray, and in so doing would be guided by statistics. 
But in judging of the probability of the straying of a 
particular dog, he would pay little heed to statistics 
as determining the chances, but would proceed upon 
empirical knowledge of the character of the dog and 
his master. Even in betting on the field against a 
particular horse, the bookmaker does not calculate 
from numerical data such as the number of horses 
entered or the number of times the favourite has been 
beaten : he tries to get at the pedigree and previous 
performances of the various horses in the running. 
We proceed by calculation of chances only when we 
cannot do better. 



Chapter X* 

INFERENCE FROM ANALOGY^ 

The word Analogy was appropriated by Mill, in accor- 
dance with the usage of the eighteenth century, to 
designate a ground of inference distinct from that on 
which we proceed in extending a law, empirical or 
scientific, to a new case. But it is used in various 
other senses, more or less similar, and in order to 
make clear the exact logical sense, it is well to specify 
some of these. The original word dvaXoyia, as em- 
ployed by Aristotle, corresponds to the word Proportion 
in Arithmetic : it signified an equality of ratios, lo-6Trj<: 
Xoyiov: two compared with four is analogous to four 
compared with eight. There is something of the same 
meaning in the technical use of the word in Physiology, 
where it is used to signify similarity of function as 
distinguished from similarity of structure, which is 
called homology : thus the tail of a whale is analogous 
to the tail of a fish, inasmuch as it is similarly used 
for motion, but it is homologous with the hind legs of 
a quadruped; a man's arms are homologous with a 
horse's fore legs, but they are not analogous inasmuch 
as they are not used for progression. Apart from 
these technical employments, the word is loosely used 
in common speech for any kind of resemblance. Thus 
De Quincey speaks of the " analogical '* power in 
memory, meaning thereby the power of recalling things 

(367) 



368 Inductive Logic^ or the Logic of Sciena. 

by their inherent likeness as distinguished from their 
casual connexions or their order in a series. But even 
in common speech, there is a trace of the original 
meaning: generally when we speak of analogy we 
have in our minds more than one pair of things, and 
what we call the analogy is some resemblance between 
the different pairs. This is probably what Whately 
had in view when he defined analogy as " resemblance 
of relations ". 

In a strict logical sense, however, as defined by 
Mill, sanctioned by the previous usage of Butler and 
Kant, analogy means more than a resemblance of 
relations. It means a preponderating resemblance 
between two things such as to warrant us in inferring 
that the resemblance extends further. This is a 
species of argument distinct from the extension of an 
empirical law. In the extension of an empirical law, 
the ground of inference is a coincidence frequently 
repeated within our experience, and the inference is 
that it has occurred or will occur beyond that experi- 
ence : in the argument from analogy, the ground of 
inference is the resemblance between two individual 
objects or kinds of objects in a certain number of 
points, and the inference is that they resemble one 
another in some other point, known to belong to the 
one, but not known to belong to the other. " Two 
things go together in many cases, therefore in all, 
including this one," is the argument in extending a 
generalisation : " Two things agree in many respects, 
therefore in this other," is the argument from analogy 

The example given by Reid in his Intellectual Powers 
has become the standard illustration of the peculiar 
argument from analogy. 

We may observe a very great similitude between this 



Inference from Analogy. 369 

earth which we inhabit, and the other planets, Saturn, 
Jupiter, Mars, Venus and Mercury. They all revolve round 
the sun, as the earth does, although at different distances 
and in different periods. They borrow all their light from 
the sun, as the earth does. Several of them are known to 
revolve round their axis like the earth, and by that means 
have like succession of day and night. Some of them have 
moons, that serve to give them light in the absence of 
the sun, as our moon does to us. They are all, in their 
motions, subject to the same law of gravitation as the earth 
is. From all this similitude it is not unreasonable to think 
that these planets may, like our earth, be the habitation 
of various orders of living creatures. There is some proba- 
bility in this conclusion from analogy.^ 

The argument from analogy is sometimes said to 
range through all degrees of probability from certainty 
to zero. But this is true only if we take the word 
analogy in its loosest sense for any kind of resemblance* 
If we do this, we may call any kind of argument an 
argument from analogy, for all inferences turn upon 
resemblance. I believe that if I throw my pen in the 
air it will come down again, because it is like other 
ponderable bodies. But if we use the word in its 
limited logical sense, the degree of probability is much 
nearer zero than certainty. This is apparent from the 
conditions that logicians have formulated of a strict 
argument from analogy. 

I. The resemblance must be preponderating. In 
estimating the value of an argument from analogy, we 
must reckon the points of difference as counting against 
the conclusion, and also the points in regard to which 
we do not know whether the two objects agree or 
differ. The numerical measure of value is the ratio of 

^ Hamilton's Rttd^ p. 356. 
24 



ijo Inductive LogU^ or the Logic of Science, 

the points of resemblance to the points of difference 
plus the unknown points. Thus, in the argument that 
the planets are inhabited because they resemble the 
earth in some respects and the earth is inhabited, the 
force of the analogy is weakened by the fact that we 
know very little about the surface of the planets. 

2. In a numerical estimate all circumstances that 
hang together as effects of one cause must be reckoned 
as one. Otherwise, we might make a fallaciously 
imposing array of points of resemblance. Thus in 
Reid's enumeration of the agreements between the 
earth and the planets, their revolution round the sun 
and their obedience to the law of gravitation should 
count as one point of resemblance. If two objects 
agree in a, b^ Cj d^ e^ but b follows from a, and d and e 
from ^, the five points count only as two. 

3. If the object to which we infer is known to 
possess some property incompatible with the property 
inferred, the general resemblance counts for nothing. 
The moon has no atmosphere, and we know that air is 
an indispensable condition of life. Hence, however 
much the moon may resemble the earth, we are 
debarred from concluding that there are living creatures 
on the moon such as we know to exist on the earth. 
We know also that life such as it is on the earth is 
possible only within certain limits of temperature, and 
that Mercury is too hot for life, and Saturn too cold, no 
matter how great the resemblance to the earth in other 
respects. 

4. If the property inferred is known or presumed to 
be a concomitant of one or more of the points of 
resemblance, any argument from analogy is superfluous. 
This is, in effect, to say that we have no occasion to 
argue from general resemblance when we have 



Inference from Analogy, 371 

reason to believe that a property follows from some- 
thing that an object is known to possess. If we knew 
that any one of the planets possessed all the conditions, 
positive and negative, of life, we should not require 
to reckon up all the respects in which it resembles 
the earth in order to create a presumption that it is 
inhabited. We should be able to draw the conclusion 
on other grounds than those of analogy. Newton's 
famous inference that the diamond is combustible is 
sometimes quoted as an argument from analogy. But, 
technically speaking, it was rather, as Professor Bain 
has pointed out, of the nature of an extended generalisa- 
tion. Comparing bodies in respect of their densities and 
refracting powers, he observed that combustible bodies 
refract more than others of the same density; and 
observing the exceptionally high refracting power of 
the diamond, he inferred from this that it was com- 
bustible, an inference afterwards confirmed by experi- 
ment. "The concurrence of high refracting power 
with inflammability was an empirical law ; and 
Newton, perceiving the law, extended it to the adjacent 
case of the diamond. The remark is made by Brewster 
that had Newton known the refractive powers of the 
minerals greenockite and octohedritey he would have 
extended the inference to them, and would have been 
mistaken.*' ^ 

From these conditions it will be seen that we cannot 
conclude with any high degree of probability from 
analogy alone. This is not to deny, as Mr* Jevons 
seems to suppose, that analogies, in the sense of 
general resemblances, are often useful in directing 
investigation. When we find two things very much 
8ilike» and ascertain that one of them possesses a 
^ Bain's LogU, ii. 145. 



372 Inductive Logic^ or the Logic of Science. 

certain property, the presumption that the other has 
the same is strong enough to make it worth while 
trying whether as a matter of fact it has. It is said 
that a general resemblance of the hills near Ballarat 
in Australia to the Californian hills where gold had been 
found suggested the idea of digging for gold at Ballarat. 
This was a lucky issue to an argument from analogy, 
but doubtless many have dug for gold on similar 
general resemblances without finding that the resem- 
blance extended to that particular. Similarly, many 
of the extensions of the Pharmacopeia have proceeded 
upon general resemblances, the fact that one drug 
resembles another in certain properties being a suffi- 
cient reason for trying whether the resemblance goes 
further. The lucky guesses of what is known as 
natural sagacity are often analogical. A man of wide 
experience in any subject-matter such as the weather, 
or the conduct of men in war, in business, or in 
politics, may conclude to the case in hand from some 
previous case that bears a general resemblance to it, 
and very often his conclusions may be perfectly sound 
though he has not made a numerical estimate of the 
data. 

The chief source of fallacy in analogical argument 
is ignoring the number of points of difference. It 
often happens that an amount of resemblance only 
sufficient for a rhetorical simile is made to do duty as 
a solid argument. Thus the resemblance between a 
Iving body and the body politic is sometimes used to 
support inferences from successful therapeutic treat- 
ment to State policy. The advocates of annual 
Parliaments in the time of the Commonwealth based 
their case on the serpent's habit of annually casting 
its skin. 



Inference from Analogy. 373 

Wisest of beasts the serpent see» 
Just emblem of eternity, 

And of a State's duration ; 
Each year an annual skin he takes, 
And with fresh life and vigour wakes 

At every renovation. 

Britain ! that serpent imitate. 

Thy Commons House, that skin of Stats^ 

By annual choice restore ; 
So choosing thou shalt live secure, 
And freedom to thy sons inure, 

Till Time shall be no more. 



Carlyle's saying that a ship could never be taken 
round Cape Horn if the crew were consulted every 
time the captain proposed to alter the course, if taken 
seriously as an analogical argument against Represen- 
tative Government, is open to the objection that the 
differences between a ship and a State are too great 
for any argument from the one to the other to be of 
value* It was such fallacious analogies as these that 
Heine had in view in his humorous prayer, " Heaven 
defend us from the Evil One and from metaphors ". 



PRINTED AT THE EDINBURGH PRESS, 9 AND II YOUNG STREET 



678 ^ 




A 



\0 °<, - 







V « 












xoo^ 






>-^^^._ . 



S ^ -- , V- '^ .0 H ■ \V 









» ^ ' <jO 



^0 o^^ 










,p .-^^ >^ J^yivy^^ ^ . <\: Deacidified using the Bookkeeper proi 

^^ \' ^ j^^^^CA\ -^ '^ r^\ =^ j: Neutralizing agent: IVIagnesium Oxide ^ 



A -r. >- %' 




'■ Treatment Date: Sept. 2004 



,/ PreservatioiiTechnologies 



A WORLD LEADER IN PAPER PRESERVATION 

1 1 1 Thomson Park Drive ,'J| 

Cranberry Township. PA 16066 '^m 
(724) 779-21 1 1 ^ 




























\ 







LIBRARY OF CONGRESS 




013 064 702 9 






